Multi-stage multi-bet game, gaming device and method

ABSTRACT

A game is comprised of a plurality of stages. Each operation of the game begins with the operation of a first stage. Depending on the outcome of the first stage the game may be over, or there may be an operation of a second stage. Depending on the outcome of the second stage, the game may be over or there may be an operation of another stage. This sequence continues until the game ends or until the final (n th ) stage has been operated, at which time the game ends. Wagers are made on successive stages of the multi-stage game. Each stage of the game may typically have its own paytable or payout scheme, and its own expected return. A bet made on a stage of the game which is not played is lost in the preferred form of the invention. One embodiment is a three stage, multi-line, multi-coin video slot machine. The same game format (slots) with the same paytable is operated on three stages, with increasing payout multipliers at each stage providing an increasing amount to win at the higher stages. The “spin” at each stage is independent of the previous stages. The second embodiment is a multi-stage Five-Card Stud poker game. Each stage is again independent of the previous stage. A variation of this game is also shown which uses the same paytable on each stage, but combined with a mechanism to increase the “hit” rate. A third embodiment is a Draw poker game that combines the concepts of the Stud poker embodiment with the decisions and optimal play analysis that are integral to Draw poker. The fourth embodiment is a dice game which has been adapted to provide a high dependency between the first stage and the next stages.

FIELD OF THE INVENTION

[0001] This invention relates to games in general, and particularly togaming machines allowing wagers to be placed on a game, and moreparticularly to an innovative casino-type gaming machine which allowswagers on a plurality of game levels.

DISCUSSION OF THE PRIOR ART

[0002] There are many ways in which multiple wagers may be placed ondifferent gaming machines. In one of the simplest forms, a player maymake a variable wager on a specific bet. On a single line slot machinefor example, as the player inputs additional coins into the machine (perplay) the payouts for the single payline is multiplied by the number ofcoins bet. Often the higher awards increase beyond the given multiple,offering a bonus for betting more coins on this single payline. The sametype of multiple coin bet is also well known in video poker, where atypical bet is one to five coins on each hand played. In such a videopoker game, the paytable is multiplied by the number of coins bet with asubstantial bonus being given for a Royal Flush when five coins are bet.

[0003] In other gaming machines, there are multiple bets that can bemade on different outcomes. In a multiline slot machine for example, awager can be made on each of a plurality of paylines. Typically, eachpayline is paid according to a paytable (also referred to as a “payouttable”) that is similar for each payline. A single spin of the reelsyields a result on each payline which is paid if it matches a winningcombination on the paytable.

[0004] The above two techniques have been combined, providing multiplepaylines and multiple coins per payline. The pay for each payline ismultiplied by the number of coins bet on that payline with certainbonuses available when a higher number of coins per payline are wagered.

[0005] Additionally, there have been games such as Double-Down Studpoker which allow a player to place an additional bet on a game that isalready in progress. There have been games such as Play-It-Again pokerwhich allow a player to make a new bet on a re-play of a starting hand.

[0006] Thus, it can be appreciated that there have been poker games, forinstance, which allow a player to bet on multiple hands where each ofthe plurality of hands is generated from a single initial deal, followedby independent draws or re-deals for each hand that received a bet. Ineach case, the bets that are made are considered to be made on a game ofchance, and paid if there is a winning result.

SUMMARY OF THE INVENTION

[0007] In broad overview, the present invention in one aspect allows theplacing of multiple bets on different stages of a game. The game iscomprised of a plurality of stages. Each operation of the game beginswith the operation of a first stage. Depending on the outcome of thefirst stage the game may be over, or there may be an operation of asecond stage. The second stage operation may be totally independent ofthe first stage, or may have dependencies on first stage events or data,e.g., the achievement of a “winning” first stage. As will be understoodthroughout this invention disclosure, “winning” is just one form ofpossible advancement to the next level. For example, one aspect of theinvention includes a “special card” (Free Ride) which permitsadvancement even if a “losing” condition is presented at a level.

[0008] Depending on the outcome of the second stage, the game may beover or there may be an operation of a third stage. This sequencecontinues until the game ends or until the final (n^(th)) stage has beenoperated, at which time the game ends.

[0009] It should be appreciated that not every stage will operate ineach game, and that the lowest stages will operate the most often whilethe highest stages will operate the least often.

[0010] As noted above, the present invention furthermore allows theplayer to place wagers on different stages of the multi-stage game. Eachstage of the game may typically have its own paytable or payout scheme,and its own expected return. A bet made on a stage of the game which isnot played is lost in one contemplated form of the invention. Thus, atthe highest stages the bets made are lost very often, without evenplaying that stage of the game, because most games will end beforegetting to the highest stage bet. Due to this architecture, there ismuch greater opportunity for large wins in games which get to thehighest stages. This makes for a more exciting gaming experience,because as the players watch the game successfully continue through thevarious stages, the expectation of what may be won at each stage usuallyincreases.

[0011] Embodiments shown herein are generally constructed such that theplayer specifies at the outset of the game the number of stages orlevels to bet on. For instance, bets are made on a first level, a secondlevel, and up to the number of levels specified by the player. Whilethis is one preferred embodiment which gives the player action at alllevels up to the highest level bet, it is envisioned that the playercould be allowed to arbitrarily choose which levels to bet withoutdeparting from the invention. So too, it is contemplated that the gamecould allow for a new bet as stages are achieved.

[0012] Certain contemplated embodiments also have a structure that any“Win” on a given stage advances the game to the next stage. Othercontemplated embodiments have different game rules for continuing fromstage to stage, and operate under those rules for a given stage.

[0013] In one aspect of the invention, it is a principal objective toprovide a method of playing a game, where a player is initially providedwith a first stage game of chance upon which a first wager is placed bythe player, and a second stage game of chance upon which a second wageris placeable. As previously noted, the game stages can be the same typeof game (e.g., slots), or different games (e.g., slots, cards, dice,roulette, etc.).

[0014] Each stage has a “winning” condition and a “losing” condition.That is, there is an established criterion or criteria whereby theplayer may advance from one stage to the next, or may not. As usedthroughout this disclosure, and in the claims, “winning” and “losing”are to be considered synonymous with advancing or terminating, unlessotherwise stated.

[0015] The first stage game is played, with a determination of whether awinning/advancement or losing/terminating condition is presented. If awinning condition is presented by the first stage game as played, thenthe player advances to the second stage game, assuming a bet has beenpreviously placed for that stage. If a losing condition is presented bythe first stage game as played, however, the game is over and any secondwager (or higher) is lost. It will be understood that in someembodiments a loss condition could be presented by simply achieving acondition where only part of a wager placed on a given level may bereturned, i.e., a player wagered 5 on a level but only achieved a returnof 3. So too, all of the bet need not be lost as a terminating/losingcondition.

[0016] In the event that the first stage presents a winning conditionand there is a wager for the second stage, then the second stage game isplayed. There follows a determination as to which of the winning andlosing conditions is presented by the second stage game as played. Thesesteps are repeated for as many stages as are provided by the game if allhave been bet upon, or as many stages as have actually been bet upon iffewer than all, again assuming a winning/advancement condition has beenmet for each preceding stage.

[0017] In a preferred form the foregoing method of playing a gameincludes the step of providing a payout for a winning condition at thesecond stage, or more preferably providing a payout for a winningcondition at each stage. The payout can be based upon the amount of arespective wager at a respective stage, and advantageously includes anincrease by a multiplier for a payout at a respective stage, with themultiplier increasing for each successive stage.

[0018] In another aspect of the invention, the foregoing method isadapted for operating a processor-controlled gaming machine. In thisapplication of the invention, gameplay elements are provided in a mannerthat can be visualized by a player, such as on a video display screen,or in some three dimensional format where the gameplay elements can betracked (such as on a board with an electronic interface), just to nametwo ways of such visualization. In this form of the invention, amechanism for a wager input from the player is also provided, along witha mechanism for game operational input from the player, such as to startplay.

[0019] There is a first stage game of chance upon which a first wager isplaced by the player, and at least a second stage game of chance uponwhich a second wager is placeable. Each stage has a winning/advancementcondition and a losing/terminating condition. In the preferred form ofthe invention, all wagers are placed before play begins at the firststage level.

[0020] This gaming machine displays at least the first stage game usingat least some of the gameplay elements. For instance, using a videomonitor as an example, a first slot machine may be displayed (or firstdisplay of cards, or dice, etc.). More than one stage may be displayedat a time (e.g., a plurality of slot machine representations stacked oneon top of another on the display). The first stage game is then played,with the previously described determination of which of the winning andlosing conditions is presented by the first stage game as played. Again,if a winning condition is presented, the player advances to the secondstage game, but if a losing condition is presented by the first stagegame as played, the game is over and at least some (and most preferablyall) of the second (and any subsequent) wager is lost.

[0021] If not already displayed, and assuming there has been anadvancing condition met at the first stage and a bet placed on thesecond stage, the second stage game of chance is displayed (or, forinstance, activated if already displayed). This second stage is played,with a determination of which of the winning and losing conditions ispresented by the second stage game as played. If there is a winningcondition, this form of the invention provides a payout for the secondstage, as well as for any subsequent consecutive stage for which thereis a winning condition, and a wager placed thereon.

[0022] One embodiment of this method as applied to a gaming machineprovides a set of differing gameplay element indicia, such as facets ofa die. A subset of at least one match indicia against which a set ofdice are to be matched in the course of play is established, such as arandom selection of die faces (e.g., three die numbers against whichtossed dice are to be matched. In a preferred form of this dice gamingmachine, first, second, third and successive stages up to said n^(th)stages are displayed together as discrete arrays on a visual display.

[0023] The dice are initially tossed in one embodiment, and beginningwith at least the second stage game, a determination is made as towhether any match is made between the match indicia and the dice tossed.At least one match comprises a winning condition for a stage beingplayed, in this embodiment. If a match is not made, then the unmatchedindicium is removed from further play. The game ends when no matches aremade at a given level, again assuming that a wager has been made up toand including that level.

[0024] Yet another aspect of the invention is providing a feature whichis subject to random allocation to a stage in the course of play, withthe feature if allocated enabling a next stage to be played regardlessof whether a winning condition has otherwise been presented. Thefeature, referred to herein as a “Free Ride,” therefore constitutes orcomprises a so-called winning/advancement condition. Of course, a wagerstill needs to have been placed on the next stage which is subject tobeing so enabled for play by the Free Ride feature.

[0025] A video card game comprises yet another form of the invention.Here, a video display device is driven by a cpu having a program. Awager input mechanism registers a wager placed by a player, with thewager including an ability to register bets upon successive stages ofthe game. A first deck of playing cards comprised of cards of suit andrank is generated by the program, with the program establishing a firstarray for display of a subset of the deck (i.e., a hand) of cardsrandomly selected from the deck.

[0026] A first stage hand of cards is dealt. The card game could be onein which the hand as so dealt is not subject to a draw, or the playercan select cards to discard, with a new card taking the place of anydiscarded. In either event, the hand ultimately becomes set, and adetermination is made as to whether the hand of cards presents awinning/advancement condition based upon a preset hierarchical rankingof card arrangements relating to suit and rank. As in the situationsnoted above, subsequent hands of cards are dealt if a winning conditionis presented by the previous hand, provided a bet has been registeredfor each successive stage. If a losing condition is presented by astage, or a stage is reached upon which no wager has been made, the gameis over. Bets on any higher stage are lost if a losing condition ispresented, as is the bet on the stage for which the losing condition isregistered. A payout output based upon the wager and predeterminedvalues for a stage is preferably provided according to a presethierarchical ranking of card arrangements relating to suit and rank. Thepayout output can include payout tables which are different for at leastsome of the stages, and may further include a multiplier for at leastsome of the stages, with the multiplier increasing for successivelyhigher stages.

[0027] In a video slot machine version of the invention, a plurality ofrotatable reels is generated by the computer program, each of the reelsbeing comprised of a plurality of different indicia. Each of the reelsis caused by the program to appear to rotate and then randomly stop tothereby yield a display of certain indicia as a spin. If an advancementcondition is presented on the first stage spin, a second stage spinoccurs if a bet has been registered for that second stage spin, and soforth. The first stage spin can be visually displayed as a first set ofreels in a first array, with the second stage spin likewise visuallydisplayed as a second set of reels in a second array, and successivestage spins each so displayed as further sets of reels in successiverespective arrays, with a plurality of arrays being displayed togetheron the visual display. Alternatively, one set of reels could berepeatedly spun for each stage. Payouts and multipliers can be providedin like manner to that described above for the card game embodiment, oras otherwise may be desired. One variant of the slot machine version ofthe invention has the multiplier for the games n^(th) stage spin (thelast possible level) randomly selected by the program from apredetermined table of multipliers, where at least most of themultipliers are greater than a multiplier for any previous stage. Thisrandom multiplier can advantageously be displayed, or physicallyembodied, as a wheel having segments with the multipliers displayed inrespective segments of the wheel. The wheel is caused to rotate and cometo a stop with the random multiplier at a designated stop point.

[0028] Of course, the foregoing invention as described in a video slotmachine embodiment could be readily embodied in a standard mechanicalslot machine. Likewise, the video dice game is readily adapted to atable-type game format, as is the video card game contemplated above.

[0029] In the same vein, a gaming machine coming within the scope of oneaspect of the invention broadly comprises a gaming unit having at leastfirst and second stages of play, each stage having an advancementcondition and a non-advancement condition. Some kind of interfacemechanism with the gaming unit allows gameplay input for a player, withthe gameplay input including wagering input allowing the player toregister a bet upon one or more stages of play.

[0030] An operational device operates the gaming unit, upon player inputincluding an operational command. The operational device determineswhich of the conditions is presented by a first stage as played, and ifan advancement condition is presented, then advancing the gaming unit tothe second stage, but if a non-advancement condition is presented, thegame is over and at least a portion, and preferably all, of any secondstage bet registered is lost. Play continues for a successive stage upto a predetermined n^(th) stage if an advancement condition isdetermined for that next stage to be reached, and a bet has beenpreviously registered for that successive stage. Again, the stages ofplay can be games which are of the same type of game, or different typesof games. These can also be games that have not yet been invented.

[0031] These aspects of the invention, along with other aspects,advantages, objectives and accomplishments of the invention, will befurther understood and appreciated upon consideration of the followingdetailed description of certain present embodiments of the invention,taken in conjunction with the accompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

[0032]FIG. 1 is a video screen representation highlighting threepaylines of a stage of a video slot machine embodiment of the presentinvention;

[0033]FIG. 2 is a video screen representation similar to FIG. 1highlighting five paylines;

[0034]FIG. 3 is a video screen representation of a three stage slotmachine embodiment of the present invention;

[0035]FIG. 4 is a representation of a paytable of winning combinationsfor the slot machine presented in FIG. 3;

[0036]FIG. 5 is a representation of a continuation of the paytable ofFIG. 4;

[0037]FIG. 6 is another video screen representation of the slot machineembodiment of FIG. 3 of the present invention;

[0038]FIG. 7 is another video screen representation of the slot machineembodiment of FIG. 3;

[0039]FIG. 8 is another video screen representation of the slot machineembodiment of FIG. 3;

[0040]FIG. 9 is another video screen representation of the slot machineembodiment of FIG. 3;

[0041]FIGS. 10a-10 e present a flow chart of a method of operating athree stage video slot machine gaming machine of the type of embodimentof FIG. 3;

[0042]FIG. 11 is a representation highlighting a bonus multiplier wheelfor use in a video slot machine embodiment of the present invention;

[0043]FIGS. 12a-12 c present flow charts of a method of operating avideo slot machine gaming machine embodiment of the present inventionusing the bonus multiplier wheel of FIG. 11;

[0044]FIG. 13 is a video screen representation highlighting amulti-stage poker gaming machine embodiment of the present invention;

[0045]FIG. 14 is a video screen representation highlighting a firststage result on the poker machine embodiment of FIG. 13;

[0046]FIG. 15 is a video screen representation highlighting a secondstage of the poker machine embodiment shown in FIG. 13;

[0047]FIG. 16 is a video screen representation highlighting a thirdstage of the poker machine embodiment of FIG. 13;

[0048]FIG. 17 is a video screen representation highlighting anothermulti-stage poker gaming machine embodiment of the present invention;

[0049]FIG. 18 is a representation of a paytable of winning combinationsof the poker gaming machine embodiment of FIG. 17;

[0050]FIG. 19 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

[0051]FIG. 20 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

[0052]FIG. 21 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

[0053]FIG. 22 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

[0054]FIG. 23 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

[0055]FIG. 24 is a video screen representation of the poker gamingmachine embodiment of FIG. 17, but with a different opening hand shownusing a “Free Ride” card;

[0056]FIG. 25 is another video screen representation of the poker gamingmachine embodiment of FIG. 24;

[0057]FIG. 26 is another video screen representation of the poker gamingmachine embodiment of FIG. 24;

[0058]FIGS. 27a-27 f present a flow chart of a method of operating adraw poker video gaming machine of the present invention;

[0059]FIG. 28 is a video screen representation of a multi-stage videodice gaming machine embodiment of the present invention;

[0060]FIG. 29 is a video screen representation highlighting a firststage or roll of the dice of the dice gaming machine embodiment of FIG.28;

[0061]FIG. 30 is a video screen representation of a second stage of theplay of the dice gaming machine embodiments of FIG. 28;

[0062]FIG. 31 is a video screen representation of a third stage of theplay of the dice gaming machine embodiment of FIG. 28;

[0063]FIG. 32 is a video screen representation of a fourth stage of theplay of the dice gaming machine embodiment of FIG. 28;

[0064]FIG. 33 is another video screen representation of the dice gamingmachine embodiment of FIG. 28; and

[0065]FIGS. 34a-34 d present flow charts for a method of operating avideo dice gaming machine of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0066] Four different embodiments of the present invention are describedherein, with some noted variations in certain cases. The firstembodiment is a three stage, multi-line, multi-coin video slot machine.The same game format (slots) with the same paytable is operated on threestages, with increasing payout multipliers at each stage providing anincreasing amount to win at the higher stages. The “spin” at each stageis independent of the previous stages.

[0067] The second embodiment is a multi-stage Five-Card Stud poker game.Each stage is again independent of the previous stage. However, aseparate paytable is used for each stage in this embodiment. A variationof this game is also shown which uses the same paytable on each stage,but combined with a mechanism to increase the “hit” rate.

[0068] The third embodiment is a Draw poker game that combines theconcepts shown in the Stud poker game with the decisions and optimalplay analysis that are integral to Draw poker. The final embodiment is adice game which has been adapted to provide a high dependency betweenthe first stage and the next stages.

[0069] While each of these embodiments uses a single game format, ortype, to play from stage to stage, as noted above, it is clearlyanticipated that the invention may be used with a first game type as afirst stage, with a subsequent stage or stages being of a different gametype, e.g., a single line slot stage, then a multi-line slot stage, thena Stud poker stage, etc. Thus, it should be appreciated that similar ordifferent games of chance may be staged together, and the invention isnot limited to the types of games shown here, and would encompass anyconceivable other game, such as roulette, craps, baccarat, keno, and soon. It will also be apparent to one of skill in the art how to use theinvention in live games with dealers (i.e., table games),notwithstanding the particular embodiments described herein relating togaming machines.

[0070] Triple-Strike Slots

[0071] A first embodiment of this invention takes the form of amulti-stage slot machine. This may be done on a video screen with thepresentation of a video slot machine, or may be accomplished withmechanical spinning reels, for instance. In a mechanical embodiment, thestages may be played sequentially on the same reels, or on physicallyseparate reels. It is also adaptable for combinations of video slots andmechanical spinning reel slots, where some stages are played on thevideo slots and some stages are played on mechanical spinning reels.

[0072] In this first embodiment, there are three video slot machines(stages) vertically disposed on a video screen (although it will beapparent how to adapt this technique to any number of desired stages).In this embodiment, each machine has the same symbols, symbol frequency,hit rate and payout percentage. Of course, other embodiments may usedifferent hit rates and frequencies, if not entirely different symbolsand game themes from stage to stage.

[0073] In this first embodiment, the criterion for advancing from onestage to the next is any win on the current stage. It is envisioned thatother criteria may be used in other embodiments, such as a specialsymbol, which while only paying in certain configurations, would advancea player to the next level anytime it appeared in the game.

[0074] Turning now to FIG. 1, the first embodiment has each stage as afive-reel, five-line video slot machine. This is of a type of slotmachine often called “Australian style.” This machine allows the playerto make a wager on one to five paylines, and allows a bet from one tonine coins bet on each payline for a maximum of forty-five coins bet pergame. FIG. 1 shows the first three paylines, with payline 1 drawnhorizontally across the center symbols, payline two drawn across theupper symbols and payline three drawn across the lower symbols.

[0075]FIG. 2 is the same as FIG. 1, with fourth and fifth paylinesadded. The fourth payline is in the shape of the letter “V” while thefifth payline is an inverted “V”. It is well known by those skilled inthe art how to design such a machine with more or fewer paylines, andmore or fewer coins per line. It is also well known in the art, andenvisioned for this type of game, to include special bonuses or bonusrounds for certain symbol combinations. Certain combinations have beenincluded for this purpose in the present description, but the specialbonuses and bonus rounds have been replaced by fixed awards for clarityof presentation.

[0076]FIG. 3 shows a screen with three stages displayed. For each gameplayed, the player selects from one to fifteen paylines (i.e., fivepaylines times three stages) to play or “activate”. The player operatesthe machine by pressing (actuating) buttons through the use of atouchscreen display, some pointing device, or through the use ofcorresponding mechanical pushbutton switches. The player may repeatedlypress the “Select Lines” button 12 in FIG. 3 to select one to fifteenlines. One may also press the “Select 5 Lines”, “Select 10 Lines” or“Select 15 Lines” buttons (14, 15 and 16, respectively) to select alllines of the first, first and second or all three machines respectively.As used herein, “machine” refers to each separate slot display 18, 19,20 (which will variously be referred to as machine, stage and level).Selecting from one to five lines will activate the lines on the lowermachine 18 and allow a “spin” (play) on the lower machine 18. Selectingfrom six to ten lines will activate the five lines on the lower machineand one to five lines on the second machine 19. This will then allow aspin on the first machine 18; if there is any winner on the firstmachine 18, a spin on the second machine will then follow. All amountswon on the second machine 19 are multiplied by two (2×) in this version(see window 22).

[0077] Selecting from eleven to fifteen lines will activate the fivelines on the first machine 18, the five lines on the second machine 19and from one to five lines on the third machine 20. This will then allowa spin on the first machine 18, and if there is a winner on the firstmachine, then a spin on the second machine 19 (with 2× payoutfollowing). If there is any winner on the second machine 19, that willallow a spin on the third machine 20. All amounts won on the thirdmachine 20 are multiplied by four (4×) in this version (see window 23).

[0078] In this particular embodiment, the “hit rate” (percentage ofgames that have any win) is carefully set just over 50%. This allowseach stage (18, 19 and 20) to have a multiplier that is twice that ofthe previous stage, and result in a reasonable expected payout for theplayer and reasonable expected return for the operator (e.g., gamingestablishment). More stages could be added in a manner described withoutdeparting from the invention. Also, vastly different hit rates andmultipliers could be used, separate paytables for each stage that do notscale evenly may be used, and other variations thereon will be readilyapparent to those of skill in this art.

[0079] It should be noted that bets on the second machine 19 (lines sixthrough ten) and the third machine 20 (lines eleven through fifteen)will be lost if a machine at a stage (level) below it does not result ina win, in this embodiment. This is considered offset in the mind of theplayer by game multipliers (2× and 4× respectively) when these machinesdo get a chance to spin. This increased opportunity for winnings whenthese upper stage machines get to spin adds a great deal of excitementand anticipation for the player.

[0080] Once the player has selected the number of lines, he or shespecifies how many coins are to be wagered for each of the selectedlines. As is well known in the art, all payouts are multiplied by thenumber of coins bet per payline. The player may repeatedly press the“Coins Per Line” button 25 (FIG. 3) to select one to ninecoins-per-line. The total bet is the product of the number of linesselected (button 12) and the number of coins-per-line, and is shown inthe “Total Bet” meter 26.

[0081]FIG. 4 and FIG. 5 show the paytables indicating the availablewinning combinations and rules governing those combinations. Thesepaytables may be displayed at any time by pressing the “Pays” button 28(shown, e.g., in FIG. 3). The “Help” button 29 may be pressed at anytime for an overall description of the rules of the game and itsoperation. Again, these buttons, their operation and relatedprogramming, are well known.

[0082] Once the specifics of the bet are selected as described above,the player presses the “Spin Reels” button 30, which will initially spinthe reels on the first slot machine 18. If there is no winningcombination on any active (bet) payline then the game is over and theentire bet is lost, including any amount bet on the other machines 19,20. If there is any winning combination on an active payline of thefirst machine 18, then the machine display will first show all winningpaylines followed by a pattern of cycling through the individual winningcombinations.

[0083]FIGS. 6 and 7 show how the game cycles through multiple winningcombinations of the first machine 18. In FIG. 6, the single “WILD”symbol is shown as a winner on payline 1. The machine draws boxes, forinstance, around the winning symbols on the payline. In the payoutinformation window 21 to the right of the first machine 18, the top linecalls out “Line 1: 2 Coins”. This indicates the two coins awarded forone “WILD” symbol on payline 1, as confirmed by the paytable in FIG. 4.After showing the display of FIG. 6 for a few seconds, the machine showsthe display of FIG. 7, which calls out the next winning combination.FIG. 7 shows three cow symbols on payline 5 (in boxes). The top line ofthe payout information window 21 now calls out “Line 5: 5 Coins” inrecognition of the five coins won for the three cows on the fifthpayline (confirmed by the paytable in FIG. 5).

[0084] For both FIG. 6 and FIG. 7, the second line of the payoutinformation window 21 shows the total number of coins from all pays ofthe first machine (in this case “SubTotal: 7” consisting of the twocoins from the first payline and the five coins from the fifth payline).The lower half of the payout information window 21 then shows the totalpay of the machine, times the machine multiplier, which for the firstmachine is one (1×).

[0085] This results in a “Total” of seven coins for the lower machine.The “Total Won” meter 36 on the right edge of the screen shows thisseven coin figure in FIG. 7. FIG. 6 and FIG. 7 show the second machine19 “lit up” and ready to spin as a result of the win on the firstmachine 18.

[0086] As a result of winning on machine 18, the player is now allowedto spin the reels of the second machine 19, provided that a bet wasplaced on at least one of lines six through ten. The reels on the secondmachine 19 are spun by again pressing the “Spin Reels” button 30. Ifthere is no winning combination on the reels of the second machine 19,then the game is over. In that case, any bet made on the third machine20 (lines eleven through fifteen) is lost, and the winnings from thefirst machine 18 are paid to the player. The game pays the awardedcredits from first machine 18 then restarts, becoming ready to takeanother bet.

[0087] In the case of a winning combination on the second machine 19,then it may have an overall display similar to FIG. 8. With only asingle winning combination on the second machine, the machine boxes the“7's” symbol on its first payline, and shows in the second stage, payoutinformation window 22 that one coin was won for a “SubTotal” of one coinon the second machine 19. Since all pays on the second machine aremultiplied by two in this version (multiplier 2×), this results in atotal pay of two coins on the second machine 19. The “Total Won” meter36 is now updated to nine coins, which comprises the seven coins wonfrom the first machine 18, plus the two coins won from the secondmachine. Since the player bet five coins on the second machine 19 (oneeach on lines six through ten), this second machine result is actually anet loss of three coins. However, because it was not a total loser (zerocoins won), the player is now entitled to spin the third machine 20 if abet was placed on any of lines eleven through fifteen. FIG. 8 shows thethird machine 20 lit up and ready to spin as a result of the two coinwin on the second machine.

[0088] Once again, the reels on the third machine are spun by pressingthe “Spin Reels” button 30. If there is no winning combination on thereels of the third machine 20, then the game is over. In that case, thewinnings from the two other machines are paid to the player, and thegame recycles for a new bet.

[0089] A winning combination is shown on the third machine 20 in FIG. 9.With only a single winning combination on the third machine 20, themachine boxes the three “7's” symbols on its first payline, and shows inthe third stage payout information window 23 that twenty-five coins werewon, for a “SubTotal” of twenty-five coins on the third machine 20.Since all “pays” on the third machine are multiplied by four (multiplier4X for this version), this results in a total pay of one hundred coinson the third machine 20. The “Total Won” meter 36 is now updated to 109coins, to include the 100 coins won from the third machine. With thethird and final machine having been played, the total winnings of 109coins are now added to the total credits meter 37, and the game is readyto restart and receive another bet.

[0090] The “Max Bet Spin” button 39 (shown in FIGS. 3 through 9)provides a one touch solution which will cause all fifteen lines to beselected with nine coins bet per line and spin the reels on the firstmachine 18, assuming enough credits are available. It is the same aspressing the “Select Lines” button 12 until “15” is selected, thenpressing the “Coins Per Line” button 25 until “9” is selected, then“Spin Reels” button 30.

[0091] The above-described embodiment of a gaming slot machine isoperationally summarized in the flow charts of FIGS. 10A-E. FIG. 10Agenerally describes the start-up of the Triple-Strike Slots game. First,an assessment of whether credit(s) are present is undertaken beginningat step 150. If none is present, then a check is made as to whether theplayer has inserted the relevant coin, credit card, etc., for thenecessary credit(s) at step 151. If so, then at step 152 the credit(s)are registered and displayed at the “Total Credits” meter 37 (e.g., FIG.3). All available player buttons are then activated for initiation ofplay at 155.

[0092] At this stage, the player enters a set-up loop where the playermay choose to add more credits or proceed with play at step 156. Ifcredits are added, these are registered (on the meter display 37) atstep 158, and the program loops back to step 156 (via 155).

[0093] The “Coins Per Line” button 25 can alternatively be engaged fromstep 156, causing the coins-per-line setting to be modified (asindicated at meter 40, FIG. 3), as well as updating the value of the“Total Bet” window 26, as indicated at step 159. Once again, the programloops back to step 156.

[0094] Back at step 156, the player then can choose the lines upon whichto bet through operation of general “Select Lines” button 12. Thiscauses the graphics program to highlight the lines being designated atstep 160. Alternatively, the special “Select Lines” buttons 14 through16 could be used out of step 156, also resulting in a registration ofthe line group selected (at step 161), then an update of the graphics atstep 160.

[0095] From step 160, the number of lines bet is registered on lines-betmeter 41 (e.g., FIG. 3), and updated if the lines bet has been modifiedup or down, as indicated at step 162. The “Total Bet” window 26 is alsoupdated in view of the lines being bet. The player is then returned tostep 156.

[0096] Once the player has input the parameters of the wager, then the“Spin Reels” button 30 is engaged. It should be noted that the foregoingselection sequence as to coins and lines to bet need not follow theorder indicated.

[0097] The player has the option of skipping all of the line andcoins-per-line selections, through resort to the “Max Bet Spin” button39. A subroutine will then execute at step 165 to assess the totalcredits the player has provided, and determine the maximum number ofcoins per line and the maximum number of lines (per an embedded look-uptable) which can be played for the credit quantity shown in totalcredits meter 37, up to a fixed maximum for the game. The graphics areupdated accordingly at step 166 to show the lines being bet (as at step160), with a similar update of the coins-per-line meter 40, lines-betmeter 41 and “Total Bet” meter 26, all as indicated at step 167.

[0098] From either the actuation of the “Spin Reels” button 30 or the“Max Bet Spin” button 39, the selection buttons for player input arethen deactivated and the amount bet is subtracted at step 168, with theremaining credits updated on the “Total Credits” meter 37. The displaygraphics then shows the reels spinning at the first stage/level/machine18 (step 169). The reel stop positions are selected in a random manner(step 170), with the graphics displaying the final symbols coming intoview for each reel in sequence (steps 171 a through 171 e).

[0099] Turning now to FIG. 10B, the program then assesses whether thereis any winning combination presented by the reels in their stoppositions, taken in view of the paytable (FIGS. 4 and 5) and the linesbet, as indicated at step 175. If there is no winner, the game goes to a“Game Over” sequence (step 176 a), described hereafter. If there is awinner, then the winning line(s) are graphically highlighted on thedisplay (step 177), the amount won is totaled and shown in the“SubTotal” area of the first stage payout information window 21 (step178), and the “SubTotal” amount is increased by the applicablemultiplier (step 179), which in this first embodiment is IX for stageone. This total for machine one is displayed in payout informationwindow 21. The “Total Won” meter 36 is accordingly updated (step 180).

[0100] An assessment is then made as to whether the player has bet onany lines of the second stage/level/machine 19, as noted at step 182. Ifnot, then the game goes to the “Game Over” sequence (step 176 b). If astage-two bet has been registered, then the player “Spin Reels” button30 is reactivated at step 183. Machine two 19 is graphically highlightedon the display (e.g., see FIG. 6), which may include flashing the button30 or the like to alert the player to continue play (step 184).

[0101] While waiting for the player to spin the second stage (machinetwo 19), like all other points that the program waits for input, a checkis made at 187 to see if additional credits have been purchased by theplayer. If more credits are input, they are registered on the “TotalCredits” meter 37 (step 188), and the player is looped back to step 187.Ultimately, the “Spin Reels” button 30 is actuated by the player at step187, and play on the second machine 19 commences.

[0102] The button 30 is then deactivated (step 189), the second machinereels are graphically shown spinning (step 190), and the sequence ofsteps 170 and 171 a through 171 e described with respect to the firstmachine 18 is repeated, except now as related to the second machine 19,as shown in steps 191 and 192 a through 192 e.

[0103] As shown in FIG. 10C, steps 195 and 197 through 200 then repeatthe process for the second machine described in steps 175 and 177through 180, respectively, with regard to the first machine. Note thatstep 199 increases the “Sub-Total” by 2× in this version, and the payoutinformation window 22 is utilized.

[0104] If a bet has been registered for lines on the third machine 20(step 202), the “Spin Reels” button 30 is again activated (step 203),machine 20 is graphically highlighted on the display (e.g., see FIG. 8),which may include flashing the button 30 or the like to alert the playerto continue play (step 204), and the player is again given the option ofadding more credits, or alternatively simply advancing to play the thirdstage (step 207). If more credits are input, they are registered on the“Total Credits” meter 37 (step 208), and the player is looped back tostep 207. Ultimately, the “Spin Reels” button 30 is actuated by theplayer at step 207, and play on the third machine 20 commences.

[0105] The “Spin Reels” button is once more deactivated (step 209), andsteps 210, 211 and 212 a through 212 e repeat steps 169, 170 and 171 athrough 171 e, respectively, this time for the third machine 20.

[0106] As shown in FIG. 10D, steps 215 and 217 through 220 then repeatthe process for the third machine 20 described in steps 175 and 177through 180, respectively, with regard to the first machine 18. Notethat step 219 increases the “Sub-Total” by 4× in this version, and thepayout information window 23 is utilized (e.g., see FIG. 9).

[0107]FIG. 10E depicts the “Game Over” sequence out of either step 176 aor 176 b. If out of step 176 a, the program “dims” the game display witha “GAME OVER” message (step 222). An assessment is made as to whetherthere are any credits in the “Total Won” meter 36 at step 223. If not,the player is returned to the start up sequence step 150 from step 224.

[0108] If there are credits won, then the “Total Won” credits are addedto the “Total Credits” meter 37, accompanied by a bang, knocker or otherexciting sound, as indicated at step 225. If the “Game Over” sequence isengaged out of step 176 b, then the program cycles through step 225 then224, and returns to step 150.

[0109] Analysis of Certain Architecture of the Triple-Strike Slots Game

[0110] The multi-stage slot machine gaming machine embodiment beingdescribed has, as a base component, a single slot machine which is thenadapted for a plurality of stages. The first step in the construction ofthe single machine of the game is to select the paying combinations forthe stage, and then to lay out the symbols on the five reels in a mannerto achieve the desired hit rate. The “hit rate” (percentage of gameswith at least one winning combination) in this embodiment is ofimportance, because getting a hit (or any win) is the criterion used toadvance to the subsequent stage. In this first embodiment, it wasdecided to use the same machine at each stage with a doubling of therewards for each successive level. If the “hit rate” for such aconfiguration was set at exactly 50%, then the expected returnpercentage would be the same for each level. If the “hit rate” was lessthan 50%, then the player would get a lower expected return at eachsuccessive level, which is not desirable in general. Moreover, certaingaming jurisdictions require that each additional coin bet on a gamehave the same or greater expected return than the previous coin.

[0111] If the “hit rate” is set at just over 50%, then each successivestage will have a slightly greater return than the previous stage, whichis desirable to provide the player with an incentive to play more coinsper game. While it is easy to mathematically determine that the “hitrate” of any payline will be 18.64% in the described first embodiment, amore thorough analysis is needed to determine the “hit rate” when fivelines are played. This is due to multiple winners on different lines oncertain spins. While the single line “hit rate” may be mathematicallydetermined using the quantities of each symbol on each reel, thefive-line “hit rate” requires knowledge of the actual layout of eachreel strip to take into account which pays will occur.

[0112] The first embodiment described above uses reel strips with thirtystop positions laid out as shown in Table 1. TABLE 1 Reel Stop # Reel 1Reel 2 Reel 3 Reel 4 Reel 5 1 Scatter (Dice) Pumpkin Pumpkin Cow DartBoard 2 Dart Board Cow Pineapple Pineapple Cow 3 Wild Wild Wild WildWild 4 Cow Dart Board Banana Dart Board Banana 5 Banana Bonus (Drum) CowPumpkin Dart Board 6 7's Cow Pineapple Apple Pineapple 7 Pumpkin 7's 7'sDart Board Bonus (Drum) 8 Apple Bonus (Drum) Apple Bonus (Drum) Apple 9Scatter (Dice) Dart Board Banana Banana Cow 10 Cow Banana PineapplePumpkin Banana 11 Banana Cow Cow Cow Pumpkin 12 Bonus (Drum) 7's AppleDart Board Cow 13 7's Dart Board Dart Board Pineapple 7's 14 PineapplePineapple Banana Pumpkin Scatter (Dice) 15 Scatter (Dice) Bonus (Drum)Scatter (Dice) Bonus (Drum) Pineapple 16 Apple 7's Pumpkin Banana Cow 17Dart Board Cow 7's Dart Board 7's 18 Bonus (Drum) Pumpkin Scatter (Dice)Apple Pumpkin 19 Banana Dart Board Pineapple Cow Dart Board 20 PumpkinApple Apple Banana Pineapple 21 Scatter (Dice) Bonus (Drum) Bonus (Drum)Dart Board Bonus (Drum) 22 Banana Pumpkin Banana Pineapple Banana 23 CowCow Apple Bonus (Drum) Dart Board 24 Bonus (Drum) 7's Bonus (Drum) 7'sPumpkin 25 Pineapple Dart Board Pineapple Dart Board Apple 26 BananaPumpkin Banana Pumpkin Dart Board 27 Scatter (Dice) Bonus (Drum) Bonus(Drum) Pineapple Pineapple 28 7's Cow Apple Cow Scatter (Dice) 29 CowPineapple Pineapple Banana Banana 30 Pineapple Dart Board Bonus (Drum)Pumpkin Pumpkin

[0113] With thirty stops on each of five reels, there are a total of 30⁵or 24,300,000 possible combinations. To determine the “hit rate” forthis set of reel strips, a computer analysis well known to the art isused to evaluate each of the 24,300,000 combinations of the five reels.For each combination, the symbols are analyzed across each of the fivepaylines in comparison with the paytables and rules shown in FIG. 4 andFIG. 5. For each of the 24,300,000 combinations, if one or more of thepaylines has a winning combination or if a scatter pay is present, thena hit counter is incremented. The analysis shows that for the reelstrips of Table 1 with the paytable information provided in FIG. 4 andFIG. 5, 12,569,760 of the 24,300,000 combinations of the five reelsresult in a win, providing a 51.73% “hit rate.”

[0114] Table 2 shows the number of times each symbol appears on each ofthe five reels. This frequency data is used in combination with Table 3to determine the payout percentage. TABLE 2 Symbol Reel 1 Reel 2 Reel 3Reel 4 Reel 5 WILD 1 1 1 1 1 7's 3 4 2 1 2 Apple 2 1 5 2 2 Banana 5 1 54 4 Pineapple 3 2 6 4 4 Pumpkin 2 4 2 5 4 Dart Board 2 6 1 6 5 Cow 4 6 24 4 Bonus (Drum) 3 5 4 3 2 Scatter (Dice) 5 0 2 0 2 30  30  30  30  30 

[0115] Table 3 shows a table of the available “pays” along with thenecessary information to determine the payout percentage of the game. Toprovide the correct analysis, it should be clear that all “pays,” exceptthe “Scatter” pay of three “Scattered Dice” symbols, will only pay leftto right. That is, the indicated combination must be shown on successivereels starting with Reel 1 (see FIG. 1). The “WILD” symbol maysubstitute for any symbol except the “Bonus (Drum)” symbol and the“Scatter (Dice)” symbol. The “Scatter” pay will pay for three dicesymbols anywhere in the fifteen symbol visible display area. The“Scatter” pay will pay all paylines in addition to the highest pay oneach line. On each payline, only the highest combination is paid. Forthe purposes of the math table of Table 3, if there are two ways to makethe same highest pay value, then the combination using more symbols isused (e.g. “WILD-WILD-WILD-Banana-Any” is counted as four bananasinstead of three “WILDs”, both of which pay 50 coins).

[0116] The “Occurrences” column of Table 3 is created using the Table 2frequency data and enumerating each way to create that combination. Someexamples are shown for clarity:

[0117] 5 “WILD” 1×1×1×1×1=1

[0118] One “Wild” symbol on each reel results in one Occurrence of five“WILD.”

[0119] 4 “WILD” 1×1×1×1×(2+2)=4

[0120] One “WILD” symbol on each of the first four reels and either aDrum or a Dice symbol on the fifth reel (any other symbol will result infive of that symbol instead of four wild).

[0121] 3 “WILD” 1×1×1×3×30=90

[0122] One “WILD” symbol on each of the first three reels and a Drum onthe fourth reel and any symbol on the fifth reel (any other symbol but aDrum on the fourth reel results in four or five of that symbol).

[0123] 5 “7's” ((1+3)×(1+4)×(1+2)×(1+1)×(1+2))−1=359

[0124] Either a “WILD” or “7” on each reel, not counting the number ofways (one) to have five “WILDs.”

[0125] 4 “7's”((1+3)×(1+4)×(1+2)×(1+1)×(30−1−2))−(1×1×1×1×(30−1−2))=3213

[0126] The first component is the number of combinations with either a“WILD” or a “7” on each of the first four reels with any symbol except“WILD” or “7” on the fifth reel. This component includes combinationsthat have four “WILDs” which either pay as four “WILDs” or five of someother symbol, which need to be subtracted off. The second component isthe number of combinations that have four “WILDs” on the first fourreels that were part of the first component.

[0127] 3 Bananas((1+5)×(1+1)×(1+5)×(30−1−4)×30)−((1×1×1×(30−1−4)×30)=53250

[0128] The first component is the number of combinations with either a“WILD” or banana on each of the first three reels, with any symbolexcept a “WILD” or banana on the fourth reel and any symbol on the fifthreel. This component includes combinations that begin with three“WILDs,” which will pay as three “WILDs” or, four of some other symbolor five of some other symbol. The combinations with three “WILDs” aresubtracted off in the second component which includes the number ofcombinations that contain “WILD” on the first three reels, any symbolbut “WILD” or Banana on the fourth reel, and any symbol on the fifthreel.

[0129] 3 Scattered Dice (5×3)×30×(2×3)×30×(2×3)=486,000

[0130] Each of the five Dice on the first reel qualifies for the“Scatter” pay in any of three positions (upper position, center positionand lower position). This is multiplied by the thirty stops representingany position on the second reel, multiplied by the two Dice times threepositions on the third reel, multiplied by the thirty stops of thefourth reel, multiplied by the two Dice times three positions on thefifth reel.

[0131] All other counts in the “Occurrences” column are calculated in asimilar manner.

[0132] The “Probability” column for each row of Table 3 is computed bydividing the “Occurrences” in that row by the total number ofcombinations which is 24,300,000.

[0133] The EV or “Expected Value” for each row is computed bymultiplying the “Pay” amount times the “Probability” for that row. Thereturn from a single stage of this machine is computed by taking the sumof all EV entries, which is 0.906239712, or a 90.62% return. The payoutpercentage can be modified by modifying the Column 2 “Pay” values andthe corresponding paytable, as is well known in the art. The payoutpercentage may also be modified by changing the symbol frequencies shownin Table 2, and corresponding reel strips of Table 1. Care must be takento keep the “hit rate” at the desired level while changing the payoutpercentage. This is also well known in the art, and is often thepreferred method used to alter payout percentage, because when thismethod is used, the player cannot tell from the paytable which machinehas a higher return, or for that matter know for sure that machines areset at different payout percentages. TABLE 3 Pay Symbols Pay OccurrencesProbability EV 5 WILD 7500 1 4.11523E−08 0.000308642 4 WILD 200 41.64609E−07 3.29218E-05 3 WILD 50 90 3.7037E−06 0.000185185 2 WILD 55,400 0.000222222 0.001111111 1 WILD 2 529,200 0.021777778 0.043555556 57's 1000 359 1.47737E−05 0.014773663 4 7's 100 3,213 0.0001322220.013222222 3 7's 25 49,560 0.002039506 0.050987654 2 7's 2 461,7000.019 0.038 1 7's 1 2,025,000 0.083333333 0.083333333 5 Apples 500 3231.32922E−05 0.006646091 4 Apples 75 2,889 0.000118889 0.008916667 3Apples 15 28,350 0.001166667 0.0175 2 Apples 2 108,000 0.0044444440.008888889 5 Bananas 300 1,799 7.40329E−05 0.022209877 4 Bananas 508,975 0.000369342 0.018467078 3 Bananas 10 53,250 0.002191358 0.021913582 Bananas 2 237,600 0.009777778 0.019555556 5 Pineapples 250 2,0998.63786E−05 0.02159465 4 Pineapples 50 10,475 0.00043107 0.021553498 3Pineapples 10 62,250 0.002561728 0.025617284 2 Pineapples 2 227,7000.00937037 0.018740741 5 Pumpkins 200 1,349 5.55144E−05 0.011102881 4Pumpkins 50 6,725 0.000276749 0.013837449 3 Pumpkins 10 31,6800.001303704 0.013037037 5 Dart Boards 200 1,763 7.25514E−05 0.0145102884 Dart Boards 50 7,032 0.000289383 0.014469136 3 Dart Boards 10 28,2900.001164198 0.011641975 5 Cows 200 2,624 0.000107984 0.021596708 4 Cows50 13,100 0.000539095 0.026954733 3 Cows 5 78,000 0.0032098770.016049383 5 Bonus (Drum) 1000 360 1.48148E−05 0.014814815 4 Bonus(Drum) 150 5,040 0.000207407 0.031111111 3 Bonus (Drum) 50 48,600 0.0020.1 3 Scatter (Dice) 8 486,000 0.02 0.16 Losing Spin 19,771,2000.81362963 24,300,000 1 0.906239712

[0134] Building now upon the single stage machine so described, Table 4shows how the return for the multi-stage version of the game iscomputed. The first column shows the “Stage” for which the return isbeing computed. The second column shows the probability of a hit on thespecified stage. In this first embodiment, this is the “hit rate” of asingle stage of the machine, which is the criterion for moving up to thenext stage. The third column shows the probability of playing thespecified stage (as opposed to losing all bets on that stage withoutplay). This is “1” for the first stage (the first stage is alwaysplayed), and for the other stages is computed by multiplying theprobability of playing the previous stage (third column, one line above)times the probability of a hit on the previous stage (second column, oneline above). For Stage 2, this is 1×0.51727=0.51727. For the third stagethis is 0.51727×0.51727=0.26757.

[0135] The fourth column shows the multiplier for all “pays” on thespecified stage. This multiplier provides a reward that more thanoffsets the losses for the times that the stage is not played. The fifthcolumn shows the EV for the machine on the specified stage, which is thesame for each identical machine in this embodiment. The sixth columnshows the overall EV of the specified stage, and is computed bymultiplying the third through fifth columns together. This is becausethe EV of a stage (fifth column) has to be scaled up by the payoffmultiplier (fourth column) and reduced by taking into account theprobability of playing that stage (third column). The seventh columnshows the cumulative EV when one, two or three stages are played. Thisis the average of the sixth column of the specified level and all levelsabove it. When only one stage is played the cumulative EV is the same asthe EV of that stage. When two stages are played, the cumulative EV isthe average of the EV of the first stage and the second stage. When allthree stages are played, the cumulative EV is the average of the EV ofthe first stage, second stage and third stage. This results in anoverall expected return of 93.79% when all three stages (fifteen lines)are played. TABLE 4 Multiplier Cumulative Probability Probability ForPays EV of All of hit on this of Playing on this EV of EV of This Stagesup to Stage stage This Stage Stage Machine Stage this Level 10.517274074 1 1 0.906239712 0.906239712 0.90624 2 0.5172740740.517274074 2 0.906239712 0.937548616 0.921894 3 0.517274074 0.2675724684 0.906239712 0.969939184 0.937909

[0136] A Variation on Triple-Strike Slots

[0137] In a modification to the first embodiment above, a fourth stageis added allowing the player to wager on one to twenty lines. Instead ofoffering a fixed 8× multiplier on the fourth stage, however, after anywin on the fourth stage the multiplier is randomly selected from a rangeof 4× to 50×, with weighted frequencies selected such that the overallvalue of the multiplier is about 8×. Each time that a spin on the fourthstage results in any win, the game goes through a selection process thatpresents a multiplier of 4× to 50× to the player. One method ofpresentation is to select the multiplier and show it on the screen tothe player. Table 5 shows a table of weighted entries that are used forthis purpose. After a win on the fourth stage of this game, the machineuses its RNG (random number generator) to select an integer from 1 to29. This number is “looked up” in the second column of Table 5 (titled“Values”), and the corresponding value in the first column (titled“Multiplier”) is used as the stage multiplier for that spin. The thirdthrough fifth columns of Table 5 are used to determine the EV of thefourth stage multiplier in the same manner used in Table 3. TABLE 5Multiplier Values Occurrences Probability EV 50 1 1 0.03448276 1.72413825 2 1 0.03448276 0.862069 10 3-5 3 0.10344828 1.034483 8 6-7 20.06896552 0.551724 6  8-12 5 0.17241379 1.034483 5 13-25 13  0.448275862.241379 4 26-29 4 0.13793103 0.551724 29  1      8    

[0138] Table 6 is a modified version of Table 4, with the fourth stageadded showing the overall payout percentage of this modified game is95.43% with all twenty lines played. Also note that the payoutpercentage on the fourth stage is 100.34%. A bet on this particularstage has a positive expectation for the player. This bet (on linessixteen through twenty) is only allowed in conjunction with thenegative-expectation bets (i.e., less than 100%) on the first fifteenlines, thus resulting in an overall negative expectation of a 95.43%return. TABLE 6 Multiplier Probability Probability For Pays EV of All ofhit on this of Playing on this EV of EV of This Stages up to Stage stageThis Stage Stage Machine Stage this Level 1 0.517274074 1 1 0.9062397120.906239712 0.906239712 2 0.517274074 0.517274074 2 0.9062397120.937548616 0.921894164 3 0.517274074 0.267572468 4 0.9062397120.969939184 0.937909171 4 0.517274074 0.1384083 8 0.9062397121.003448787 0.954294075

[0139] To add even more excitement to the presentation of the foregoingfourth stage, another variation of this four stage game adds amechanical wheel for selection of the multiplier for wins on the fourthstage. Adams, U.S. Pat. Nos. 5,823,874 and 5,848,932, and Telnaes, U.S.Pat. No. 4,448,419, may be referred to for detail on such bonussequences and indicia. The wheel 42 shown in FIG. 11 has sixteensections, although any number of visible sections may be used. Table 7uses the same multiplier values as shown in Table 5, but allocates thesevalues to the sixteen sections of the mechanical wheel of FIG. 11.

[0140] The above-described embodiment of a gaming slot machine havingfour stages and a random number multiplier on the fourth stage isoperationally summarized in the flow charts of FIGS. 12A-12C. Theprogram for this Multi-Strike Slots variation embodiment issubstantially the same as that previously described with respect toFIGS. 10A through 10E. Accordingly, and keeping with the same conventionused throughout this application, like numbers are used to describe likesteps. The changes made to the previously-described program willtherefore only be discussed as to this version.

[0141] Turning first to FIG. 12A, Multi-Strike Slots follows the sameprogramming as set forth in the flow charts of FIGS. 10A through 10C forTriple-Strike Slots, and up through step 220. Step 232 begins a sequencefor a fourth stage/level/machine, with steps 233, 234, 237 and 238corresponding to steps 183, 184, 187 and 188, respectively, except asnow related to a fourth machine. Note that in the event of no bet on thefourth machine (step 232), a “Game Over” sequence is then engaged atstep 176 c.

[0142] As in the other levels, the “Spin Reels” button is once moredeactivated (step 239), and steps 240, 241 and 242 a through 242 erepeat steps 169, 170 and 171 a through 171 e, respectively, this timefor the fourth machine. Turning to FIG. 12B, steps 245, 247 and 248 thenrepeat the process for the fourth machine described in steps 175, 177and 178, respectively, with regard to the first machine 18.

[0143] Step 249 will now initiate a sequence for a multiplier to beapplied to the fourth level in this version. First, a number is randomlyselected from a table provided for the fourth level multiplier at step249. The bonus wheel 42 (FIG. 11) may then be graphically “spun” at step250, and stopped on the previously selected number from step 249, asindicated at step 253. A mechanical wheel of the type disclosed in U.S.Pat. Nos. 5,823,874 and 5,848,932 can likewise be advantageouslyemployed. This multiplier factor is then displayed (step 254), and the“Sub-Total” amount for the fourth level is then increased by this factorand displayed as a “Total” for the fourth machine (step 255), with thelatter sum then added to the “Total Won” meter 36 amount for display, asshown in step 256. The game then proceeds from step 256 to “Game Over”sequence 176 c. The “Game Over” sequence shown at FIG. 12C for thisversion is the same as that previously described, except for reflectingthe path from point 11 (rather than from point 9 in the previousversion). TABLE 7 Wheel Stop Multiplier Values Occurrences ProbabilityEV 1 8  1 1 0.034482759 0.275862069 2 5 2-3 2 0.068965517 0.344827586 36 4-6 3 0.103448276 0.620689655 4 5 7-9 3 0.103448276 0.517241379 5 1010-11 2 0.068965517 0.689655172 6 4 12-13 2 0.068965517 0.275862069 7 5014 1 0.034482759 1.724137931 8 5 15-17 3 0.103448276 0.517241379 9 25 181 0.034482759 0.862068966 10 4 19 1 0.034482759 0.137931034 11 10 20 10.034482759 0.344827586 12 5 21-23 3 0.103448276 0.517241379 13 8 24 10.034482759 0.275862069 14 4 25 1 0.034482759 0.137931034 15 6 26-27 20.068965517 0.413793103 16 5 28-29 2 0.068965517 0.344827586 29  1 8

[0144] Triple-Strike Stud Poker

[0145] Another embodiment uses this multi-stage game technique for theplay of video poker. This second embodiment adapts a Five-Card Stud gamewith hit rates under 50% and over 50%. The invention may also be used toadapt many other poker games, including Five-Card Draw poker, DoubleDown Stud poker (see e.g., U.S. Pat. Nos. 5,100,137 and 5,167,413) andBig Split poker (disclosed by the inventors herein in a pending U.S.patent application) among others.

[0146] In this second embodiment, there are three stages of Five-CardStud poker. This game pays on any hand that is one pair or better. Itwill be seen that about 49.88% of hands in Five-Card Stud poker rank asone pair or higher. For this game with a “hit rate” under 50%, it wouldbe undesirable to use 2× and 4× multipliers on the second and thirdstages respectively, since this would make the return of these stageslower than the first stage. This means that a player wagering more moneywould get a lower expected return, which is undesirable to theproprietor of the game who wants to encourage as high a wager aspossible, but may also run afoul of regulations in certain gamingjurisdictions, which require equal or higher return for each coinwagered on a single game. There are many ways that the game may bemodified to cause the higher stages to have a higher payout, of whichtwo will be shown here.

[0147] In the first version of this poker embodiment, a separatepaytable is used for each stage of the game, as shown in FIG. 13. InFIG. 13, it is clear that the Hand #2 (51) paytable has all pays fromthe Hand #1 (50) paytable multiplied by 2×, except for the “4 of a Kind”which goes from 50 to 200, thus providing additional return that willmore than offset the “hit rate” being under 50%. Likewise, the Hand #3(52) paytable has all pays from the Hand #2 paytable multiplied by 2×except for the “Full House”, which goes from 50 to 150, which again morethan offsets the “hit rate” being under 50%. This will become clear inthe analysis shown below, if not already evident.

[0148] Referring still to FIG. 13, the player uses the “Select Number ofHands” button 54 to select a bet on one to three hands (stages) 50, 51and 52. The game may be configured with more or less stages (number ofhands) without departing from the invention. The “Coins per Hand” button55 is then used to wager from one to five coins per hand. This range ofcoins may be modified to any acceptable range, as is well known in theart. The “Deal Hand” button 56 will cause the game to deal out Hand #1(50) from a standard fifty-two card deck of playing cards. While thisgame uses a standard deck of cards of rank and suit, other embodimentsmay use one or more “Jokers.” Still other embodiments may use certaincards, such as Deuces, as wild cards. Even more broadly, while thissecond embodiment is a poker game, other card games or different gamesof chance will be readily adaptable to use with the overall inventiveconcept, as previously noted.

[0149]FIG. 14 shows the game screen after one coin was bet on threehands, and a first stage hand has been dealt. The hand shown contains apair of 5's, which pays one coin for a “Low Pair” (highlighted on the.Hand #1 (50) paytable). The one coin won is shown in the “Total Won”meter 58. As a result of achieving any win on Hand #1, Hand #2 (51) maynow be played. If Hand #1 (50) was a loser (less than one pair), thenthe game would be over and the wagers on Hand #2 (51) and Hand #3 (52)would be lost without playing those stages.

[0150] Having won Hand #1 (50), however, the player presses the “DealHand” button 56 and a second hand is dealt as is shown in FIG. 15. Inthis hand 51, the player has received another pair of 5's, which nowpays two coins as called out in the Hand #2 (51) paytable. The “TotalWon” meter 58 is updated to three (one coin from Hand #1 plus two coinsfrom Hand #2). As a result of a win on Hand #2, Hand #3 (52) may now beplayed. If Hand #2 (51) had been a loser (less than one pair), then thegame would be over and the wager on Hand #3 lost.

[0151] The player once again presses the “Deal Hand” button 56 aftersuccess at stage two, and a third hand (52) is dealt as is shown in FIG.16. This hand has a pair of tens and a pair of deuces for “Two Pair.”The paytable shows that two pair pays twelve coins when achieved on Hand#3 (as opposed to six coins on hand #2 or three coins on hand #1). The“Total Won” meter 58 is updated to “15,” and the game is over since allhands wagered on have been played. The total win of fifteen credits isadded to the “Credits” meter 59, advancing the meter from “177” to “192”(from an arbitrary start of “180”).

[0152] Analysis of Triple-Strike Stud Poker Game

[0153] Table 8 shows how the calculation of certain architecture of thepayout percentage (expected return) of the first stage of this secondembodiment is computed. This table is for a one coin bet. It is wellknown in the art how to expand this for a higher number of coins bet perhand, and for the inclusion of bonuses for a higher number of coins.

[0154] The number of possible five card poker hands from a fifty-twocard deck is known as “52 choose 5” and is computed with the followingformula: $\frac{52!}{{5!}*{\left( {52 - 5} \right)!}} = {2,598,960}$

[0155] The first column of Table 8 shows the rank of all hands in thisFive-Card Stud game. The second column shows the pay value for thisranking on Hand #1 (each hand 50, 51 and 52 having a separate paytable).The third column (“Occurrences”) is the number of times a particularhand occurs in the 2,598,960 possible five card poker hands dealt from astandard deck. This “Occurrence” tabulation is well known to thoseskilled in the art, and may be derived by analyzing each of the2,598,960 hands with a computer program, also well known. The fourthcolumn shows the probability of playing Hand #1 when a bet is placed onthis hand. For Hand #1 this probability is 1.0, since the first handwill always be played when it is bet on. The fifth column shows theprobability of receiving the hand called out in the first column. Thisis computed by dividing the “Occurrences” (third column) by the2,598,960 total number of possible hands.

[0156] The sixth column is the product of the fourth and fifth columns,which is the probability of getting a particular hand on this stage (forthe first stage it is the same as the fifth column since the first stageis always played). The seventh column is the expected value contributionEV, which is the product of the second column pay and the sixth columnprobability of achieving the given hand on the current stage. The sum ofall EV contributions provides the expected return of 0.916288 or 91.63%.This expected return may be modified by making modifications to the“Pay” values in the second column of Table 8, as is well known in theart. TABLE 8 Probability of Probability Probability of Playing This ofThis Hand on Pay Occurrences Stage This Hand This Stage EV ROYAL FLUSH2000 4 1 1.5391E-06 1.53908E-06 0.003078 STRAIGHT FLUSH 250 36 11.3852E-05 1.38517E-05 0.003463 FOUR OF A KIND 50 624 1 0.00024010.000240096 0.012005 FULL HOUSE 25 3,744 1 0.00144058 0.0014405760.036014 FLUSH 15 5,108 1 0.0019654 0.001965402 0.029481 STRAIGHT 810,200 1 0.00392465 0.003924647 0.031397 THREE OF A KIND 5 54,912 10.02112845 0.021128451 0.105642 TWO PAIR 3 123,552 1 0.047539020.047539016 0.142617 JACKS OR BETTER 2 337,920 1 0.13002124 0.1300212390.260042 LOW PAIR 1 760,320 1 0.29254779 0.292547788 0.292548 BUST1,302,540 1 0.50117739 0.501177394 0 2,598,960 1 0.916288

[0157] Table 9 shows a similar analysis for Hand #2 (51) (the secondstage of this game). The second column now has the Hand #2 paytableshowing all values doubled from the Hand #1 paytable with the Four of aKind going from 50 to 200. The fourth column, “Probability of PlayingThis Stage” is the probability of getting any “hit” (one pair or higher)on the first stage. This is computed by adding up all of the fifthcolumn values from Table 8 except for “Bust,” or by subtracting theprobability of a “Bust” (0.50117739) from 1.0, resulting in a firststage hit rate of 0.498822606 or 49.88%. The sum of the EV components onthe second stage is 0.9261078, indicating a 92.61% expected return. Thishigher expected return than the first stage is a result of the 200 coinFour of a Kind value more than offsetting the “hit rate” which isslightly under 50%. This expected return may, again, be modified bymaking modifications to the “Pay” values. TABLE 9 Probability ofProbability Probability of Playing This of This Hand on Pay OccurrencesStage This Hand This Stage EV ROYAL FLUSH 4000 4 0.498822606 1.5391E-067.67726E-07 0.003071 STRAIGHT FLUSH 500 36 0.498822606 1.3852E-056.90954E-06 0.003455 FOUR OF A KIND 200 624 0.498822606 0.00024010.000119765 0.023953 FULL HOUSE 50 3,744 0.498822606 0.001440580.000718592 0.03593 FLUSH 30 5,108 0.498822606 0.0019654 0.0009803870.029412 STRAIGHT 16 10,200 0.498822606 0.00392465 0.001957703 0.031323THREE OF A KIND 10 54,912 0.498822606 0.02112845 0.010539349 0.105393TWO PAIR 6 123,552 0.498822606 0.04753902 0.023713536 0.142281 JACKS ORBETTER 4 337,920 0.498822606 0.13002124 0.064857533 0.25943 LOW PAIR 2760,320 0.498822606 0.29254779 0.14592945 0.291859 BUST 1,302,5400.498822606 0.50117739 0.249998614 0 2,598,960 1 0.926107

[0158] Table 10 shows a similar analysis for Hand #3 (52) (the thirdstage of this game). The second column now has the Hand #3 paytableshowing all values doubled from the Hand #2 paytable with the Full Housegoing from 50 to 150. The “Probability of Playing This Stage” is theprobability of getting any “hit” (one pair or higher) on the first andsecond stages. This is the square of the 0.498822606 “hit rate” of thefirst stage since a “hit” is required on both the first and secondstages in order to play the third stage. The fourth column value mayalso be computed by subtracting the probability of getting a “Bust” onthe first stage (0.50117739) and the probability of getting a “Bust” onthe second stage (0.249998614) from 1.0 (i.e.,1−0.50117739−0.249998614=0.248823992). The sum of the EV components onthe third stage is 0.941849, indicating a 94.18% expected return. Thishigher expected return than the second stage likewise is a result of the150 coin Full House value more than offsetting the second stage “hitrate” which is slightly under 50%. Once again, the expected return maybe modified by making modifications to the “Pay” values. TABLE 10Probability of Probability Probability of Playing This of This Hand onPay Occurrences Stage This Hand This Stage EV ROYAL FLUSH 8000 40.248823992 1.5391E-06 3.82959E-07 0.003064 STRAIGHT FLUSH 1000 360.248823992 1.3852E-05 3.44663E-06 0.003447 FOUR OF A KIND 400 6240.248823992 0.0002401 5.97417E-05 0.023897 FULL HOUSE 150 3,7440.248823992 0.00144058 0.00035845 0.053767 FLUSH 60 5,108 0.2488239920.0019654 0.000489039 0.029342 STRAIGHT 32 10,200 0.248823992 0.003924650.000976546 0.031249 THREE OF A KIND 20 54,912 0.248823992 0.021128450.005257266 0.105145 TWO PAIR 12 123,552 0.248823992 0.047539020.011828848 0.141946 JACKS OR BETTER 8 337,920 0.248823992 0.130021240.032352404 0.258819 LOW PAIR 4 760,320 0.248823992 0.292547790.072792909 0.291172 BUST 1,302,540 0.248823992 0.50117739 0.12470496 02,598,960 1 0.941849

[0159] Table 11 shows the return of betting on one, two or three stagesin this poker game of the second embodiment. For the “Stage” called outin the first column, the second column shows the EV for that stage takenfrom Tables 8, 9, and 10. The third column is the EV of an entiremulti-stage game with a bet on the number of stages in the first column.This is the average of the selected second column level and all levelsabove (i.e., the average EV of all those stages in the multi-stagegame). The expected return of the entire game when a player plays allthree stages is 0.928081203 or 92.81%. TABLE 11 EV of Game Total EVPlaying this many Stage For Stage stages 1 0.91628805 0.916288054 20.92610692 0.921197488 3 0.94184863 0.928081203

[0160] A Variation on Triple-Strike Stud Poker

[0161] This modification of the Triple-Strike Stud poker game introducesa “Free Ride” feature. This feature is used to increase the “hit rate”of the basic game without making any other modifications to the game(such as which hands pay). This feature provides a greater flexibilityin setting the “hit rate” than is available by simply setting which rankis the lowest pay. Using normal poker game construction techniques, onewould typically have to include more paying hands to increase the “hitrate.” In the game of the above second embodiment, the highest nonpayinghand to add would be “Ace High,” which would add almost 20% to the hitrate as shown in Table 12. Paying on all hands that have an Ace(referred to as “Ace High”) would bring the hit rate up from 49.88% to69.23%, which is far beyond the goal of just over 50%. Another variancecould require “Ace-King” high as the minimum hand, which would bring thehit rate to 56.32%, which is still a very large increase. TABLE 12 Sumof Hit Rate at Occurrences Occurrences this rank ROYAL FLUSH    4 40.00% STRAIGHT FLUSH   36 40 0.00% FOUR OF A KIND   624 664 0.03% FULLHOUSE  3744 4408 0.17% FLUSH  5108 9516 0.37% STRAIGHT  10200 197160.76% THREE OF A KIND  54912 74628 2.87% TWO PAIR 123552 198180 7.63%JACKS OR BETTER 337920 536100 20.63% LOW PAIR 760320 1296420 49.88%ACE-KING 167280 1463700 56.32% ACE HIGH 335580 1799280 69.23% BUST799680 2598960 100.00% 2,598,960   

[0162] In this modified embodiment, a “Free Ride” feature is added tothe game wherein in some of the hands, on a random basis, a “Free Ride”indicia will be displayed, advantageously with an accompanying sound.When the “Free Ride” is indicated, the hand will be dealt as usual andpaid according to the paytable, but the game will automatically advanceto the next hand that was wagered on, whether or not the player wins thecurrent hand.

[0163] Using this feature, multiple stages of this game can beconstructed with a natural hit rate under 50%, yet use the same paytablefor all stages with multipliers for each stage.

[0164] Another advantage of the “Free Ride” feature is that it is notnecessary to modify paytable values to increase the “hit rate.” It iswell known in the art that as additional “pays” are allowed to increasethe “hit rate,” other pay values or frequencies will need to bedecreased to offset the amount paid out on the new values. The “FreeRide” introduces a method of raising the “hit rate” of a game withoutany other modification to the payout of the game through the use of“hits” that award no coins/credits. This is important for the purpose ofadapting games with paytables that are already familiar to the players.It is also a valuable tool that gives the game designer more flexibilityin the creation of a game.

[0165] Table 8 is still representative of the first stage of this “FreeRide” version. In this modified embodiment, the “Free Ride” is offeredon sixteen of every one thousand hands (based on a random number foreach hand), or 1.6% of the hands played. This will increase the “hitrate” of the stage. Using more than 1.6% “Free Rides” will provide agreater increase, while using less than 1.6% will provide a smallerincrease in the “hit rate.” Because the “Free Ride” offers no benefitwhen playing on the highest hand that has been wagered on (there beingno “next hand” to advance to) it is not offered on the final hand.

[0166] Table 13 shows how the “hit rate” is determined for the firststage of Table 8 that includes a 1.6% “Free Ride.” The first line showsthe “hit rate” that is achieved for first stage hands, 0.4988. Thesecond line shows the sixteen in one thousand probability of the “FreeRide” being offered. The third line shows the probability of losing onthe first stage. This is the “Bust” probability taken from Table 8. Thefourth line is the product of the second and third lines, showing theprobability of getting a “Free Ride” on a “Busted” hand. This is theadditional “hit rate” component, since winning hands that receive theFree Ride are already figured into the first line. The fifth line is thesum of the first and fourth lines and is the resulting “hit rate” forthe first stage including the “Free Ride” feature which is 0.506841 or50.68%. TABLE 13 Hit Rate for Hands of First Stage 0.498823 Free RideProb. 0.016 First Stage Busts 0.501177 Free Ride Hits 0.008019 FirstStage Hit Rate w/Free Ride 0.506841

[0167] The second stage of the “Free Ride” variation is now representedby Table 14, which is similar to Table 9. The differences are in the“Pay” values, which are now exactly twice (2× multiplier) the “Pay”values from Table 8, and the fourth column “Probability of Playing ThisStage”, which is now the 0.506841 value, computed in Table 13. TABLE 14Probability of Probability Probability of Playing This of This Hand onPay Occurrences Stage This Hand This Stage EV ROYAL FLUSH 4000 40.506841444 1.5391E-06 7.80068E-07 0.00312 STRAIGHT FLUSH 500 360.506841444 1.3852E-05 7.02061E-06 0.00351 FOUR OF A KIND 100 6240.506841444 0.0002401 0.000121691 0.012169 FULL HOUSE 50 3,7440.506841444 0.00144058 0.000730144 0.036507 FLUSH 30 5,108 0.5068414440.0019654 0.000996147 0.029884 STRAIGHT 16 10,200 0.506841444 0.003924650.001989174 0.031827 THREE OF A KIND 10 54,912 0.506841444 0.021128450.010708775 0.107088 TWO PAIR 6 123,552 0.506841444 0.047539020.024094743 0.144568 JACKS OR BETTER 4 337,920 0.506841444 0.130021240.065900153 0.263601 LOW PAIR 2 760,320 0.506841444 0.292547790.148275344 0.296551 BUST 1,302,540 0.506841444 0.50117739 0.254017474 02,598,960 1 0.928826

[0168] The third stage for the “Free Ride” variation is represented byTable 15, which is similar to Table 10. Again, the differences are inthe “Pay” values, which are now exactly twice (2× multiplier), the “Pay”values from Table 14, and the fourth column “Probability of Playing ThisStage”, which is now 0.25688825, which is the square of the 0.506841“hit rate” of the first stage. TABLE 15 Probability of ProbabilityProbability of Playing This of This Hand on Pay Occurrences Stage ThisHand This Stage EV ROYAL FLUSH 8000 4 0.25688825 1.5391E-06 3.95371E-070.003163 STRAIGHT FLUSH 1000 36 0.25688825 1.3852E-05 3.55834E-060.003558 FOUR OF A KIND 200 624 0.25688825 0.0002401 6.16779E-050.012336 FULL HOUSE 100 3,744 0.25688825 0.00144058 0.000370067 0.037007FLUSH 60 5,108 0.25688825 0.0019654 0.000504889 0.030293 STRAIGHT 3210,200 0.25688825 0.00392465 0.001008196 0.032262 THREE OF A KIND 2054,912 0.25688825 0.02112845 0.005427651 0.108553 TWO PAIR 12 123,5520.25688825 0.04753902 0.012212215 0.146547 JACKS OR BETTER 8 337,9200.25688825 0.13002124 0.033400929 0.267207 LOW PAIR 4 760,320 0.256888250.29254779 0.075152089 0.300608 BUST 1,302,540 0.25688825 0.501177390.128746584 0 2,598,960 1 0.941535

[0169] Finally, Table 16 is a similar table to Table 11, showing theoverall payout percentage of the one, two and three stage versions ofthis “Free Ride” game. The increase in overall payout is a little over1.2% when going from one to three stages. This range may be increasedusing a higher “Free Ride” percentage, or decreased using a lower “FreeRide” percentage. One skilled in the art will appreciate that changingthe payout range using this independent “Free Ride” percentage providesmuch better precision and flexibility for setting this range than thepaytable modification method used in the unmodified second embodiment.TABLE 16 EV of Game Total EV Playing this many Stage For Stage stages 10.91628805 0.916288054 2 0.92882552 0.922556787 3 0.94153454 0.928882704

[0170] Multi-Strike Five-Card Draw Poker

[0171] Five-Card Draw poker is a very popular casino game and is offeredin many variations including Jacks or Better, Joker Poker, Deuces Wildand various “bonus” type Jacks or Better versions, among others. Whileit is within the scope of the invention to use any poker game withpaytables and/or multipliers that provide the increased reward on thehigher stages, or to use different variations of poker or even othergames of chance on different levels, this third embodiment will use awell known game with its well known paytables. It will also usemultipliers to increase the reward on the higher levels.

[0172] Many of the popular Five-Card Draw poker games have hit rates inthe 40% to 50% range, including Jacks or Better, Deuces Wild and themany “bonus” poker variations that are popular today in the marketplace.Since most gaming jurisdictions require that video poker be played froma “fair” deck of cards, it has become widely known that a player candetermine the payout percentage of a video poker machine by looking atits paytable. This has resulted in a growing popularity of this type ofgame. In this embodiment of the invention, a multiple stage Five-CardDraw poker game is constructed, also using the “Free Ride” featurepreviously discussed to maintain the familiar paytable. It will be shownthat the frequency of the “Free Ride” feature can be used to achieve asimilar payout percentage in the multi-stage game as the player mayexpect from the familiar paytable.

[0173]FIG. 17 shows the current (third) embodiment four-stage 9-6 Jacksor Better game. The game uses the familiar paytable shown in FIG. 18,which may be displayed by pressing the “Pay Table” button 65 shown inFIG. 17. The player presses the “Select Number of Hands” button 66 todesignate a bet on one to four hands (stages) of this game. This thirdembodiment of course may be constructed with a lesser or greater numberof stages than four, without departing from the invention.

[0174] The player presses the “Coins per Hand” button 67 to select a betranging from one to five coins per hand. Those skilled in the artunderstand how to allow the range of coins bet to be broader or narroweror how to add bonuses for higher bets.

[0175] The “Total Bet” is the product of the “Select Number of Hands”and “Coins per Hand” values, and is displayed in the “Total Bet” window68. The player then presses the “Deal/Draw” button 70 to deal out a handon the first stage 71. The buttons shown in FIG. 17 are video buttonsfor use with a touchscreen display. A pointing device such as a mouse ortrackball, physical pushbutton switches and the like may be used inaddition to or instead of the video buttons shown. If the player wishesto bet the maximum twenty coins on a game, he or she may press the “MaxBet Deal” button 76 which has the same result as pressing the “SelectNumber of Hands” button 66 until “4” is shown, followed by pressing the“Coins per Hand” button 67 until “5” is shown, followed by pressing the“Deal/Draw” button 70.

[0176] After receiving the initial hand, the player may hold one or morecards by using the touchscreen to indicate which cards are to bediscarded. FIG. 19 shows the display after the player elects to holdonly the Jack of Spades 80 from the hand dealt in FIG. 17. FIG. 19 showsthe word “Held” above the Jack of Spades 80 that was selected to beheld. The player then presses the “Deal/Draw” button 70 to replace theother four cards.

[0177]FIG. 20 shows a possible result of the draw. The draw results in aThree of a Kind. The Three of a Kind awards three coins as shown in theFIG. 18 paytable. The three coin award multiplied by the Hand #1 (71)multiplier of IX is shown to total three coins in the first stage payoutinformation window 84 to the right of Hand #1 in FIG. 20. This threecoin sub-total is shown in the “Total Won” meter 85 of FIG. 20. If Hand#1 was a loser instead of getting “Jacks or Better” (as was accomplishedwith a hand of Three of a Kind), the game would be over and the bets onHand #2 (72), Hand #3 (73) and Hand #4 (74) would be lost withoutplaying those hands.

[0178] However, as a result of obtaining a winning hand, the bet made onHand #2 (72) will now be played. Five cards are dealt randomly from aseparate (new) deck of fifty-two cards in the Hand #2 position. FIG. 20shows that the cards dealt to Hand #2 (72) include a pair of Queens 81,which already ranks above the “Jacks or Better” level required to win. Askilled player would hold the pair of Queens, and press the “Deal/Draw”button 70.

[0179]FIG. 21 shows one possible result of this second draw. In FIG. 21,a third Queen was drawn to Hand #2 resulting in Three of a Kind, whichas seen on Hand #1, awards three coins. FIG. 21 shows that this threecoin award is multiplied by the 2× multiplier for Hand #2, which resultsin a six coin total win from Hand #2. The coins awarded are shown in thesecond stage payout information window 87 to the right of Hand #2 (72).The “Total Won” meter 85 is now updated to show nine coins won, which isthe sum of the three coins won on Hand #1 and the six coins won on Hand#2. If Hand #2 was a loser instead of getting “Jacks or Better” (as wasaccomplished with a hand of Three of a Kind), the game would be over andthe bets on higher level hands would be lost.

[0180] Since a winning hand was achieved on Hand #2, the bet made onHand #3 (73) will now be played. Five cards are again dealt randomlyfrom a new deck in the Hand #3 position (73). FIG. 21 shows that thecards dealt to Hand #3 include two pair, which already is above the“Jacks or Better” level required to win. A skilled player would hold thetwo pair and press the “Deal/Draw” button 70.

[0181]FIG. 22 shows one possible result of this third draw. In FIG. 22,Hand #3 was not improved, resulting in two pair which awards two coins.FIG. 22 shows that this two coin award is multiplied by the 4×multiplier for Hand #3, which results in an eight coin total win fromHand #3. These numbers are shown in the third stage payout informationwindow 88 to the right of Hand #3 (73). The “Total Won” meter 85 is nowupdated to show seventeen coins won, which is the sum of the three coinswon on Hand #1, the six coins won on Hand #2 and the eight coins won onHand #3.

[0182] As a result of obtaining a winning hand on Hand #3, the bet madeon Hand #4 (74) will now be played. Five cards are again dealt randomlyfrom a new deck in the Hand #4 (74) position. FIG. 22 shows that thecards dealt to Hand #4 include three Jacks, which already is above the“Jacks or Better” level required to win. The three Jacks are held by theplayer and the “Deal/Draw” button 70 is again pressed.

[0183]FIG. 23 shows one possible result of this fourth draw. In FIG. 23,Hand #4 (74) becomes a Full House as a result of drawing a pair offours. A Full House awards nine coins as seen in FIG. 18. FIG. 23 showsthat this nine coin award is multiplied by the 8× multiplier for Hand#4, which results in a seventy-two coin total win from Hand #4. Thesenumbers are shown to the right of Hand #4 (74) in the fourth stagepayout information window 89. The “Total Won” meter is now updated toshow eighty-nine coins won which is the sum of coins won on all levels.The game is over as a result of playing all hands on which bets wereplaced. The credits shown in the “Total Won” meter 85 are added to the“Total Credits” window 77 taking this value to “285.”

[0184] Multi-Strike Five-Card Draw Poker with “Free Ride”

[0185] In another example of the foregoing embodiment of Five-Card Drawpoker, the same “Free Ride” feature that was described for Five-CardStud poker is used to increase the hit rate without having to modify thepopularly known paytable. FIG. 24 shows that the “Free Ride” card 90 wasdealt to the player in Hand #1 (71). The game makes an exciting soundwhen the card is dealt to alert the player that Hand #2 (72) will beavailable whether or not a win is achieved on Hand #1. After showing theFIG. 24 display for a few seconds to allow the special sound tocomplete, the “Free Ride” card 90 is replaced by another randomlyselected card and the remainder of the hand is dealt to the player inusual fashion.

[0186]FIG. 25 shows this completed hand along with a “Free Ride”indicator 91 on the left edge of the screen. As in the previous example,the player will hold desired cards and draw replacements for those cardsnot held. A skilled player would hold the 7, 10 and Jack of Diamonds,and then press the “Deal/Draw” button 70.

[0187]FIG. 26 shows that the cards drawn did not result in a win. Thefirst stage payout information window 84 now shows a zero coin win with“Free Ride” being indicated as the reason for advance. As a result ofthe “Free Ride” on Hand #1 (71), five cards are now dealt for Hand #2(72). Play would continue from level to level as long as there is awinning hand, or “Free Ride” on each level, as previously described.

[0188] Analysis of Certain Architecture of the Multi-Strike Five-CardDraw Poker Game

[0189] Part I—Review of “Standard Video Poker”

[0190] This analysis is of a “standard video Draw poker” game, whichwill then be related to Multi-Strike Five-Card Draw poker for a one coinwager per hand. It is well known by those skilled in the art how toexpand this to more coins bet, and how to add bonuses for higher bets.

[0191] Those skilled in the art of video poker development know that aFive Card Draw poker game with the paytable shown in Table 17 has anexpected return of 99.54398%.

[0192] This payout percentage is what the game will return in the longrun with “Optimal Play”. This game is usually referred to as 9-6 Jacksor Better. This is because most Jacks or Better games (without Four-ofa-Kind bonuses) use the same paytable except for the Full House andFlush awards which are modified to change the payout percentage. It iswell known that a 9-6 Jacks or Better (awarding nine coins for FullHouse and six coins for Flush) provides a 99.54% return. TABLE 17 HandRank Pay Occurrences Probability EV Royal Flush 800 64.34574832.47583E−05 0.019806614 Straight Flush 50 284.1410173 0.0001093290.005466437 Four of a Kind 25 6140.161736 0.002362546 0.059063642 FullHouse 9 29919.76638 0.011512207 0.103609866 Flush 6 28626.222360.011014491 0.066086948 Straight 4 29184.62522 0.011229348 0.04491739Three of a 3 193489.1896 0.074448699 0.223346096 Kind Two Pair 2335990.6964 0.129278902 0.258557805 Jacks or Better 1 557697.91250.214585031 0.214585031 Bust 0 1417562.939 0.545434689 0 2598960 10.99543983

[0193] Unlike the previous embodiments, Draw poker has a skill elementthat requires decisions by the player on each hand. The game is designedsuch that the payout percentage will be reached over the long run whenthe game is played optimally. Each non-optimal play lowers the expectedreturn (although it could result in a higher short term result). Each ofthe 2,598,960 possible hands may be played thirty-two ways by holdingnone, or any combination of the five initial cards dealt. Using expectedvalue analysis of the thirty-two combinations can determine the bestplay for any given hand. One skilled in the art is readily able toconstruct the table in Table 17 by writing a computer program thatperforms this analysis on each of the 2,598,960 hands.

[0194] To further clarify this method, one of the possible 2,598,960hands is examined, and in particular, the hand shown in FIG. 19: Jack ofSpades, 10 of Hearts, 9 of Diamonds, 8 of Clubs and 4 of Hearts. To findthe best way to play a hand, one computes the expected value of each ofthe thirty-two ways to play the hand. Here, two of the thirty-two waysto hold the hand of FIG. 19 are analyzed. In one case, the Jack-10-9-8four card straight is held. The second case will be holding just theJack of Spades.

[0195] Table 18 shows the expected return for holding the Jack-10-9-8four card straight. The first two columns show all possible rankings andtheir pay value. The third column shows the number of occurrences ofeach of these possible ranks when drawing to this exact situation (i.e.,given the initial five cards, the cards that were held and the suits andrank of the remaining forty-seven cards). The computation of this thirdcolumn may be exhaustively determined by analyzing each possibleresulting hand, but is usually done by an analysis of the combinationsof the held and remaining cards, which may be computed more quickly. Inthis example of drawing one card, it is easy to see that any of the fouroutstanding Queens or 7's result in eight possible straights, and thethree outstanding Jacks would result in a pair of Jacks. All other drawcards would result in a “Bust”. The fourth column shows the“Probability” of drawing to the specified rank, which is computed bydividing the third column “Occurrences” count by the forty-seven totalways to draw this hold combination. The fifth column “EV” is the productof the “Pay” value of second column and the “Probability” value offourth column. The sum of EV components results in a 0.744681 expectedreturn for this play. That is, on average, this hold will yield 74.47%of the amount bet in the long run. TABLE 18 (Expected Value of HoldingJack-10-9-8 from the FIG. 19 Hand) Hand Rank Pay Occurrences ProbabilityEV Royal Flush 800 0 0 0 Straight Flush 50 0 0 0 Four of a Kind 25 0 0 0Full House 9 0 0 0 Flush 6 0 0 0 Straight 4 8 0.17021277 0.680851 Threeof a Kind 3 0 0 0 Two Pair 2 0 0 0 Jacks or Better 1 3 0.063829790.06383 Bust 0 36  0.7659574 0 47  1 0.744681

[0196] Table 19 shows a similar analysis for the case where just theJack is held from the same hand shown in FIG. 19. The “Occurrences”column now, involves 178,365 different resulting hands when only 1 cardis held. This number of combinations is “47 choose 4” which is stated bythe formula: $\frac{47!}{{4!}*{\left( {47 - 4} \right)!}} = {178,365}$

[0197] This specifies the number of combinations of forty-seven cardstaken four cards at a time. As stated above, these “Occurrences” arefound by a well known/readily obtained computer program that eitherexhaustively analyzes each of the 178,365 draw combinations inconjunction with the Jack of Spades, or by an analysis of thecombinations of the held and remaining cards. The expected return ofholding the Jack of Spades is computed in Table 19 in a manner similarto that used in Table 18, resulting in a 47.93% expected return in thelong run. Analyzing the other thirty ways to play this hand results inan even lower expected return than the “Jack Hold” of Table 19.Therefore, the best play for this particular hand is to hold the fourcard Straight analyzed in Table 18. TABLE 19 (Expected Value of HoldingOnly the Jack in FIG. 19 Hand) Hand Rank Pay Occurrences Probability EVRoyal Flush 800 1 5.60648E−06 0.004485 Straight Flush 50 3 1.68194E−050.000841 Four of a Kind 25 52 0.000291537 0.007288 Full House 9 2880.001614667 0.014532 Flush 6 491 0.002752782 0.016517 Straight 4 5480.003072352 0.012289 Three of a Kind 3 4102 0.022997785 0.068993 TwoPair 2 8874 0.049751913 0.099504 Jacks or Better 1 45456 0.2548482050.254848 Bust 0 118550 0.664648333 0 178365 1 0.479298

[0198] The analysis program that iterates over each of the 2,598,960hands finds the best of the thirty-two possible holds, and keeps arunning sum of the expected return for these optimal holds (for thesample hand of FIG. 19, 0.744681 would be added to this sum). The sum ofall optimal hold expected returns is then divided by 2,598,960 todetermine the expected return for the game. The fifth column of Table 17shows this result of 0.99543983 along with the contribution from eachtype of hand.

[0199] Part II—Modification of Analysis for Multi-Strike Game

[0200] In playing a multi-stage Draw Poker game of the presentinvention, the optimal hold is no longer necessarily the hold that willprovide the highest expected return for the current hand, but is ratherthe hold that will provide the highest expected return on the remainderof the multi-stage game (including the current hand). As with standardDraw poker, the expected return of thirty-two hold combinations must beexamined. The expected return of any hold combination now has twocomponents. The first component is the expected return of the currenthand (which is the expected return as calculated in Table 18, times thecurrent stage multiplier). The second component is the expected returnof the remainder of the game given that hold combination. The secondcomponent is the product of the “Probability” of any win on the currentstage (for the current hold combination) and the expected return ofremaining stages. This sum may be represented as:

EV _(ch)=(EV _(std) *MULT _(stage))+(HR _(ch) *EV _(remain));where  EQUATION 1

[0201] EV_(ch)=Expected Value of current hold;

[0202] EV_(std)=Expected Value using standard analysis such as done inTable 18;

[0203] MULT_(stage)=Stage Multiplier, which is a constant for eachstage;

[0204] HR_(ch)=“Hit rate” (probability of any win) of current holdcombination; and

[0205] EV_(remain)=Combined expected return of all stages above thecurrent level that have received a bet, which is a constant for eachstage.

[0206] Simply stated, the second component is the value of “stayingalive” by getting any win. For certain hands at certain stages, it willbe advantageous to hold a combination with a lower EV_(std) due to itshigher HR_(ch).

[0207] The EV_(remain) component drives an analysis of the game from the“top down.” That is, for games with four stages bet, the analysis isdone for the fourth stage, then using the result from the fourth stageto set the EV_(remain) value, the analysis may be done for the thirdstage and so on. For each stage, EV_(remain) is a constant valuedetermined from the analysis of the stage above it.

[0208] For the fourth stage, the second component of the Equation 1 sumdrops out, because EV_(remain) is zero since there are no subsequentstages. This means that the EV_(ch) for any given hold is eight timesEV_(std), which means that standard 9-6 strategy is optimal, and willprovide a return of 0.99543983*8=7.96351864.

[0209] Before looking at the third stage analysis, it is important tounderstand the effect of the “Free Ride” feature. For the examples givenhere, a “Free Ride” rate of seventy-three per one thousand hands isused, or 7.3%. This value was carefully selected to arrive at a total“hit rate” (natural plus “Free Ride”) of slightly over 50%, as will beshown later. Those skilled in the art will see that this rate may beincreased or decreased as desired to affect the “hit rate” and expectedreturn. The “Free Ride” is randomly selected for 7.3% of the hands whenthere is a bet on a higher hand. On hands that receive a “Free Ride”card, the second component of the Equation 1 sum becomes a constant,since HR_(ch) is 1.0 for all holds (i.e., one will “hit” or advance tothe next level 100% of the time regardless of the hold combination).This means that the best hold combination for hands that have been givena “Free Ride” will match the standard strategy.

[0210] To analyze the first three stages, one looks at each of the2,598,960 possible initial five card hands. For each hand, thethirty-two possible hold combinations will need to be analyzed todetermine the best EV_(ch) hold using Equation 1 and the best standardplay hold using the method of Table 18 (EV_(std)). For many hands, thesame hold will yield the highest EV_(ch) and the highest EV_(std). Theexpected return for a given initial hand is now given by Equation 2:

EV ₁₂₃=(FR _(off) *EV _(chbest))+(FR _(on)*((EV _(stdbest) *MULT_(stage))+(1.0* EV _(remain)))); where  EQUATION 2

[0211] EV₁₂₃=Expected return for a given initial hand on Levels 1, 2 or3;

[0212] FR_(off)=Probability of not receiving “Free Ride” (0.927 for thisexample);

[0213] EV_(chbest)=EV_(ch) from hold that yields highest value inEquation 1;

[0214] FR_(on)=Probability of receiving “Free Ride” (0.073 for thisexample);

[0215] EV_(stdbest)=EV of best hold combination using standard (Table18) analysis;

[0216] MULT_(stage)=Stage Multiplier, which is a constant for eachstage; and

[0217] EV_(remain)=Combined expected return of all stages above thecurrent level that have received a bet, which is a constant for eachstage.

[0218] The first component of Equation 2 represents the hands that donot receive a “Free Ride.” The “No Free Ride” probability of 0.927 isused to weight the expected return that is computed using the formula ofEquation 1. The second component represents the hands that receive a“Free Ride. The “Free Ride” probability of 0.073 is used to weight thereturn that will result by using the standard 9-6 strategy when a “FreeRide” is awarded on this hand.

[0219] For Levels one through three, the expected return is computed byadding the EV₁₂₃ values for each of the 2,598,960 possible startinghands and dividing by 2,598,960. This expected return has the return oflevels above it embedded within its value.

[0220] It is helpful to look at how EV_(chbest) is found for aparticular hand. For the hand shown in FIG. 19, we now use the data fromTable 18 and Table 19 to compare the Ev_(ch) for the hold of the fourcard Straight vs. holding the Jack on the third stage. To do this we useEquation 1:

EV _(ch)=(EV _(std) *MULT _(stage))+(HR_(ch) *EV _(remain))  [EQUATION1]

[0221] Taking the Hit Rate (HR_(ch)) for holdingJack-10-9-8=1−(36/47)=0.234043 (from Table 18):

[0222] Hold Jack-10-9-8:EV_(ch)=(0.744681*4)+(0.234043*7.96351864)=4.84253.

[0223] The Hit Rate (HR_(ch)) for HoldingJack=1−(118550/178365)=0.335352 (from Table 19).

[0224] Hold Jack: EV_(ch)=(0.479298*4)+(0.335352*7.96351864)=4.58777.

[0225] The EV_(ch) for the other thirty hold combinations is lower thanfor holding just the Jack, therefore, EV_(chbest)=4.84253 resulting fromholding the four card Straight. From Table 18 and Table 19 it can beseen that EV_(stdbest)=0.744681 for this hand (also hold the straight).Therefore, the expected return on the third stage of this initialfive-card hand is:

EV ₁₂₃=(FR _(off) *EV _(chbest))+(FR _(on)*((EV _(stdbest) *MULT_(stage))+(1.0*EV _(remain))))  [using EQUATION 2]

EV ₁₂₃=(0.927*4.84253)+(0.073*((0.744681*4)+(1.0*7.96351864)))=5.287809

[0226] The sum of all of the EV₁₂₃ values divided by 2,598,960 for thethird stage results in an expected return of 7.95080267. This is thenumber of coins expected to be won in the remainder of any game thatreaches the third stage (i.e. return of third and fourth stagescombined).

[0227] The second stage is analyzed identically as the third stage,however EV_(remain) is now 7.95080267 and MULT_(stage) is now 2. Lookingat the hand of FIG. 19, one now has the following calculations:

Hold Jack-10-9-8: EV _(ch)=(0.744681*2)+(0.234043*7.95080267)=3.3501917

Hold Jack: EV _(ch)=(0.479298*2)+(0.335352*7.95080267)=3.6249136

[0228] When the hand of FIG. 19 is analyzed on the second stage, it isnow better to hold just the Jack rather than Jack-10-9-8, thereforeEV_(chbest) is 3.6249136. The EV_(stdbest) is still 0.744681 asJack-10-9-8 is the best standard play on any stage of the game. Theexpected return of this hand on the second level (including the expectedreturn of levels three and four) EV₁₂₃ for this hand is computed as:

EV ₁₂₃=(0.927*3.624914)+(0.073*((0.744681*2)+(1.0*7.95080267)))=4.049427

[0229] A computer program known to those of skill in the art is used tofind that the sum of all of the EV₁₂₃ values divided by 2,598,960 forthe second stage results in an expected return of 5.96916633. This isthe number of coins a player is expected to win in the remainder of anygame that reaches the second stage (i.e. return of second third andfourth stages combined).

[0230] The first stage is analyzed identically as the second and thirdstages, however EV _(remain) is now 5.96916633 and MULT_(stage) isnow 1. Looking at the hand of FIG. 19, we now have the followingcalculations:

Hold Jack-10-9-8: EV _(ch)=(0.744681*1)+(0.234043*5.96916633)=2.141723

Hold Jack: EV _(ch)=(0.479298*1)+(0.335352*5.96916633)=2.481070

[0231] When the hand of FIG. 19 is analyzed on the first stage, it isagain better to hold just the Jack rather than Jack-10-9-8, thereforeEV_(chbest) is 2.481070. The EV_(stdbest) is still 0.744681 asJack-10-9-8 is the best standard play on any stage of the game. Theexpected return of this hand on the first level (including the expectedreturn of levels two, three and four) EV₁₂₃ for this hand is computedas:

EV ₁₂₃=(0.927*2.481070)+(0.073*((0.744681*1)+(1.0*5.96916633)))=2.790063

[0232] The sum of all of the EV₁₂₃ values divided by 2,598,960 for thefirst stage results in an expected return of 3.995391. This is thenumber of coins a player is expected to win in a four stage game forwhich a four coin bet is made. Dividing this value by the four coin betresults in an expected return of 0.998848 or 99.88%. By setting the“Free Ride” percentage at 7.3% for the four stage game, the expectedreturn of 99.54% of this standard game was increased to 99.88% to give aplayer an incentive to learn the modified optimal play strategy dictatedby the EV_(ch) analysis.

[0233] In order to determine the actual amount paid out on each level aswell as the independent return of coins bet on that level, it is usefulto maintain several running sums while working through each of the2,598,960 possible hands. The following equation is calculated for eachhand, and a sum of these values is maintained:

EV _(playedhand)=(FR _(off) *EVSTD _(chbest))+(FR _(on) *EV_(stdbest))  EQUATION 3

[0234] EV_(stdbest)=EV of best hold combination using standard (Table18) analysis

[0235] EVSTD_(chbest)=Standard (Table 18) analysis EV of best hold formaximizing Equation 1.

[0236] For each hand, if there is no “Free Ride”, it will be held tomaximize EV_(ch) using Equation 1. The FR_(off) value is used to weightthe standard (Table 18 method) EV of this best hold (calledEVSTD_(chbest))). If there is a “Free Ride”, then the optimal play is tohold the combination that gives the highest standard EV. The FR_(on) isused to weight this value. For the example hand of FIG. 19, on the firststage or second stage, this would give the following equation:

EV _(playedhand)=(FR _(off) *EVSTD _(chbest))+(FR _(on) *EV_(stdbest))  [using EQUATION 3]

EV _(playedhand)=(0.927*0.479298)+(0.073*0.744681)=0.498671

[0237] The EVSTD_(chbest) and EV_(stdbest) values come from Table 19 andTable 18, respectively.

[0238] For each stage, for each of the 2,598,960 hands, theseEV_(playedhand) components are added together and the sum is divided by2,598,960. This indicates the payout of hands played on that level.These values are shown in the second column of Table 20.

[0239] In a manner similar to Equation 3, the HR_(ch) hit ratecomponents are weighted and added to result in the hit rate shown in thethird column of Table 20. The fourth column of Table 20 shows theprobability of playing a hand on a given level, which is 1.0 on thefirst level, and for the other levels, is the product of the third andfourth columns of the level below. The fifth column shows the stagemultiplier for the given level. The sixth column is the actual returnfor a particular level, which is the product of the second, fourth andfifth columns. The seventh column is expected return for the rest of agame that has reached the current stage. For the fourth stage, this isthe product of the second column (return) and fifth column (multiplier).For the lower levels, it is the product of the second and fifth columns(which represents the Expected Pay for playing the current level) plusthe third column (hit rate on current level) times the seventh column ofthe next higher level. This seventh column value is the same as the sumof the EV₁₂₃ values previously discussed. TABLE 20 Payout of ProbabilityReturn for Hands played Hit Rate of Playing Bets on this Level on thisLevel of Level Level Multiplier Level EV_(remain) 4 0.995439830.45456531 0.128598042 8 1.024092903 7.96351864 3 0.99142626 0.50041920.256980631 4 1.019109383 7.950802667 2 0.97183568 0.50630045 0.507565482 0.986540487 5.969166328 1 0.96564822 0.50756548 1 1 0.965648223.995390993 0.998847748

[0240] It is easily seen in Table 20 that on lower levels some of thecolumn 2 return is sacrificed to increase the column 3 hit rate to allowmore frequent play of the lucrative upper levels as seen in column 6.

[0241] Finally, when only two or three stages are bet, the analysis mustbe done again from the beginning, starting with the top stage andworking down. The results for two or three stages are not inferable fromthe Table 20 data, but need to be developed independently.

[0242] It should be clear that a single stage game (i.e., a bet on onlythe first level) is no different than the standard 9-6 Jacks or Bettergame.

[0243] This third embodiment of a multi-stage draw poker gaming machineis operationally summarized in the flow charts of FIGS. 27A-27F. FIG.27A generally describes the start-up of the Multi-strike Five-Card DrawPoker game embodiment, which is initially quite similar to that of thefirst (slots) embodiment. First, an assessment of whether credit(s) arepresent is undertaken beginning at step 270. If none is present, then acheck is made as to whether the player has inserted the relevant coin,credit card, etc., for the necessary credit(s) at step 271. If so, thenat step 272 the credit(s) are registered and displayed at the “TotalCredits” meter 77 (e.g., FIG. 17). All available player buttons are thenactivated for initiation of play at 275.

[0244] At this stage, the player enters a set-up loop where the playermay choose to add more credits or proceed with play at step 276. Ifcredits are added, these are registered on the meter display 77 at step277. The cards displayed from a previous hand, along with any stagetotal(s) and subtotal(s) reflected in the payout information window(s),and “Total Won” meter 85 are all cleared for the new game (step 278).The program loops back to step 276.

[0245] The “Coins per Hand” button 67 can alternatively be engaged fromstep 276, causing the coins-per-hand setting to be modified (asindicated at meter 64, FIG. 17), as well as updating the value of the“Total Bet” window 68, as indicated at step 279. Once again, the programloops back to step 276 through steps 278 and 275.

[0246] Back at step 276, the player then can choose the “Select Numberof Hands” button 66 to input this aspect of his or her wager. Thislikewise causes the “Total Bet” to be so modified, as well as displayingthe number of hands bet at meter 63, all as indicated at step 280.Graphics are also updated at step 281 to highlight the hands which arenow “active” (i.e., potentially playable). Steps 278 and 275 then followin the loop back to step 276.

[0247] Once the player has input the parameters of the wager, then the“Deal Draw” button 70 is engaged. It should be noted that the foregoingselection sequence as to coins and hands to bet need not follow theorder indicated.

[0248] The player has the option of skipping all of the hands and coinsper hand selections, through resort to the “Max Bet Deal” button 76. Asubroutine will then execute at step 285 to assess the total credits theplayer has provided, and then determine the maximum number of coins perhand and the maximum number of hands (per an embedded look-up table)which can be played for that credit quantity, up to a fixed maximum forthe game. The graphics are updated accordingly at steps 286 and 287 toshow the hands being bet, coins-per-hand and total bet (as at steps 279and 280). Steps 288 and 289 then follow, and are the same as steps 281and 278, respectively.

[0249] From either the actuation of the “Deal Draw” button 70 or the“Max Bet Deal button 76, the selection buttons for player input are thendeactivated and the amount bet is subtracted at step 291, with theremaining credits updated on the “Total Credits” meter 77. The main gameplay sequence is then begun (step 292).

[0250] The program randomly “shuffles” the deck to establish a playingorder for the fifty-two regular playing cards (used in this version) atstep 293 (FIG. 27B). A determination is made as to whether the secondstage/level/hand is “active” (bet upon) at step 295. If it is not, theprogram proceeds to step 300 described below. If it is, then asubroutine is engaged for a “Free Ride” card (this version includingthis added feature). Beginning at step 296, a random selection process(discussed above) determines whether the “Free Ride” is available ornot. If it is, then the “Free Ride” card is caused to be registered inone of the first five positions representing the order of the cards inthe shuffled deck for the cards of the first hand (step 297), and the“Free Ride” feature will be available (as, described hereafter). If itis not, then no “Free Ride” card is displayed, and the “Free Ride”feature is not available.

[0251] From either step 296 or 297, the program then “deals” (step 300)the cards for the hand, displaying the cards graphically in the fivespaces allotted in the first hand 71. A check is made in the course ofthe foregoing deal to determine if one of the dealt cards is a “FreeRide” card at step 301. If it is (i.e., the “Free Ride” feature isavailable), then the “Free Ride” card is caused to be displayed in thespace corresponding to its placement in the order, as indicated at step302. Whereupon there is an audio cue also provided, and much rejoicingis heard throughout the land (step. 303). After a suitable interval, the“Free Ride” card is caused to be replaced by the next regular playingcard in the deck order (step 304), and a “Free Ride” icon is displayednext to the level (as seen at 91 in FIG. 25).

[0252] From step 304, or step 301 if no “Free Ride” is detected, theprogram then performs an evaluation of the dealt hand (step 308) todetermine if a winning hand is presented, using the paytable hierarchydiscussed with regard to FIG. 18, or more simply, is a pair of “Jacks orBetter” presented (step 309)? If a winning hand is presented, then fromstep 309 a message is graphically displayed indicating the hand “rank”along with an audio sound acknowledging to the player that a winner isalready in hand (with or without rejoicing, as desired, rejoicing beingplayer dependent), as set forth in step 310. From either step 309 or310, the program then advances to step 315.

[0253] Step 315 provides multiple options to the player at thisjuncture. The player may choose to add more credits, for example, whichif elected results in an update to the “Total Credits” meter 77 at step314, then looping back to step 315.

[0254] The player can also choose which cards to hold/discard at thispoint. A card that is to be held is selected (step 316) and then taggedas “held” (step 317) (e.g., see FIG. 19 and related discussion). Cardspreviously selected for being held can likewise be de-selected (step318). From either step 317 or 318, the process loops back to step 315.

[0255] When the player has exercised whatever of the foregoing optionsare desired, if any, from step 315, the “Deal/Draw” button 70 is againactuated. This results in the removal from the graphic display of anycard not designated as “held” (step 320). Each card removed is replacedwith the next card in the deck order, as indicated at step 321. Are-evaluation of the hand now presented takes place at steps 322 and325, similar to that of steps 308 and 309. If a winning hand ispresented (again with reference to the paytable of FIG. 18), the type ofwinner is identified (e.g., “Three Of A Kind,”) graphically for theplayer in the payout information window 84, along with the number ofcoins/credits won as a sub-total, all as indicated in step 326. Thatsub-total is increased by the stage multiplier (which in the case of thefirst level, is IX) and displayed as a “total” for the first hand, atstep 327. From here, the first hand total is added to the “Total Won”meter amount at 85 (e.g., FIG. 20) (step 328).

[0256] If a winning hand is not presented at step 325, then a check ismade as to whether the “Free Ride” icon is registered for the level atstep 329. If it is, a message is displayed in payout information window84 that the “Free Ride” feature is being employed to advance to the nextstage/level/hand (step 330). If the “Free Ride” is not registered, thenthe game is over, and progresses to a “Game Over” sequence 331.

[0257] Out of steps 328 or 330, the program determines if the secondstage/level/hand is “active,” i.e., bet upon (step 332). If it is not,the player is sent to the “Game Over” sequence (step 331). If it isactive, however, then it is on to the next level.

[0258] Referring to FIG. 27C, play and operation continue substantiallysimilar to that described with respect to that of the first level. A“new” deck is “shuffled,” (step 333). As in the first level, adetermination is then made as to whether the third stage/level/hand is“active” (bet upon) at step 335. Steps 335 through 337, 340 through 344and 348 through 350 are the same as their respective counterpart steps(295 et seq.) discussed with regard to the play of the first hand,albeit now in view of second level play.

[0259] From step 349 or step 350, a “draw” sequence is again executed asdescribed with respect to the first hand, beginning at step 355. Thisincludes the option of adding more credits (update of credit meter atstep 354), and the selection of cards to be “held” via steps 356 through358 (corresponding to steps 316 through 318, respectively, describedabove). Once card selection is completed at step 355, previouslydescribed steps 320 through 322, and 325 through 332 are repeated, butfor this second stage/level/hand, through respective steps 360 through362, and 365 through 372. At this point, either the game is over, andthe player is routed to the “Game Over” sequence (step 371), or theplayer advances to another hand that has been bet upon, and playadvances to the third stage/level/hand out of step 372, shown in FIG.27D.

[0260] Referring now to FIG. 27D (and, e.g., FIG. 21), play continuesfor the third hand in the same manner as that described for the firstand second hands, albeit now in view of third level play. Accordingly,and for ease of description, steps described as to the first level arerelated to their corresponding steps in the third level by grouping therespective steps as follows: 293/373, 295-297/375-377, 300-304/380-384,308-310/388-390, 314-318/394-398, 320-322/400-402, 325-332/405-412. Atthis point, either the game is over, and the player is routed to the“Game Over” sequence (step 411), or the player advances to another handthat has been bet upon, and play advances to the fourth stage/level/handout of step 412, shown in FIG. 27E.

[0261] Play of the fourth hand is similar to that described above,except that no “Free Ride” is available (this being the last hand inthis particular embodiment of the game). Accordingly (and using the sameconvention for grouping like steps of the first and fourth levels forease of description), cards are “shuffled” at step 413/293, dealt atstep 420/300, and the hand is evaluated at step 428/308. If a winninghand is present (step 429/309), then a message is displayed at step430/310.

[0262] Beginning with step 435, a “draw” sequence is again executed asdescribed with respect to the first hand. In this fourth level, stepsdescribed for the first level draw sequence correspond to their fourthlevel counterparts as follows: 314-318/434-438, 320-322/440-442, and325-328/445-448. Since there is no fifth level, the game proceeds to the“Game Over” sequence out of step 448 or step 445 at step 451.

[0263] The “Game Over” sequence is set forth in FIG. 27F. A “GAME OVER”message is displayed by the graphics (step 452). The “Total Won” amount(meter 85 in FIG. 20) is checked, and if greater than zero (step 453),the credit(s) amassed as represented on the meter 85 are added to the“Total Credits” meter 87 at step 454. The player, and the game, are bothreturned to the game start up sequence out of step 453 (if nothing won)or step 454.

[0264] Bunco

[0265] Bunco, sometimes called Bunko, Bonko or Bonco, is a dice gamethat dates back to the mid 1800's in the United States. While there aremany variations that are currently played, what follows is what appearto be very popular rules of the game.

[0266] Bunco is typically played in groups of eight to twenty players,usually women and occasionally couples as a social event. A grouptypically meets once a month, and plays at multiple tables of fourplayers. Players seated across from each other are partners although itis typical to change partners for each game played. Each table has threedice that are passed around from player to player.

[0267] The game is played in “rounds”. The first round starts with alltables rolling for a “point” of one. The dice move clockwise to eachperson at the table who gets to roll the dice. A team scores one pointfor each die that matches the current point (one in this case). Eachtime one or more dice match the current point, the player's team scoresand the player continues to roll. If the player gets all three dice tomatch on a number other than the current point then that team scoresfive points and the player continues to roll. If the player gets allthree dice to match the current point they yell out “Bunco” and the teamis awarded twenty-one points.

[0268] Once a player rolls the dice showing no points, the turn ends.Each round continues with the dice going from player to player aroundthe table. The game ends when a player at the first or head tablereaches twenty-one points, which is usually indicated by ringing ahand-bell to signal all the tables that the round is over. At this pointthe players change partners and rotate through the tables based on thewinners and losers, and the next game would play with a “point” of two.

[0269] This fourth embodiment of the current invention consists of adice game that is loosely based on an individual player's turn during around of Bunco. While this game may be played in a casino with livedealers (as is done with the casino game of Craps) or on a gamingmachine that propels real physical dice, the preferred embodiment is ona video gaming machine.

[0270] Unlike the version of Bunco described above, in this fourthembodiment there may be up to three points which the player is trying toroll. Instead of being a single number, any number that has been rolledon every stage of the current game is an active point. On the firstroll, each number that appears on a die becomes a point, for a possibletotal of three points if all three dice are different (that is, all sixpossible numbers are points for the first roll). On the second roll, theplayer must roll one or more points matching the first roll to keep thegame going. Any numbers that were rolled on both the first and secondrolls remain points for the third roll. The player continues to rolluntil no dice match a number found in all previous rolls, or until thehighest stage upon which a bet has been placed is rolled.

[0271]FIG. 28 shows a display of this fourth embodiment. A maximum ofseven stages or rolls of the dice per game is provided. The game mayallow more or fewer stages without departing from the invention. Eachstage (level) of the game represents a roll of the dice as describedabove. The player may place a bet on from one to seven stages or lines.The player may bet from one to five coins per stage in this version. Ofcourse, it is anticipated that different numbers of coins per stagecould be allowed. Also, the player could be allowed to place bets ondifferent stages at random, rather than from the bottom up. For thatmatter, the player could be allowed to make different size wagers ondifferent stages at will, without departing from the invention.

[0272] Referring to FIG. 28, the “Select Lines” button 100 is pressed toselect from one to seven stages to bet on. The “Coins per Line” button101 is pressed to indicate the number of coins to bet on each line. Theplayer then presses the “Roll Dice” button 102 to roll the dice for thefirst stage.

[0273]FIG. 29 shows a game in progress after the first roll. This rollof 3-4-6 is placed in the first stage area 105 next to the applicableline of the paytable 106 for that stage (0,0,0,32). For each stage thereare four paytable values. These values are for rolling one, two or threepoints or for rolling “Bunco,” which is achieved when all three dicematch one number which is an active point. Only the highest value ispaid at each stage, so a “Bunco” does not also pay for three pointsmatched. For the first roll (with all six numbers active) anycombination of three matching dice is a “Bunco.” Scoring a “Bunco” isthe only way to win the first level bet, although in this game theplayer automatically advances to the second stage. It is envisioned thatother embodiments could set the active points in advance of the firstroll which would then require a match on the first roll to continue. Afirst stage “Bunco” awards thirty-two coins. The machine highlights theappropriate paytable value in the “3 points matched” column for thisroll and shows the remaining points under the first stage line (107).

[0274] The player presses the “Roll Dice” button 102 for the secondstage, and a possible result is shown in FIG. 30. The roll of 1-4-6matches two of the three points that were established in the first roll.Thus, the points “4” and “6” remain “alive,” i.e., in play (107). Thepoint of “3” from the first roll is no longer alive because it does notappear in the second roll. The three dice are placed on the second stageline 108 next to the applicable paytable 106 values for that stage. Thegame highlights the “2 points matched” value in the paytable indicatingthat one coin is awarded for matching two points on the second stage.The “Total So Far” meter 110 is updated to show the total of one coinwon at this point (zero coins on the first stage and one coin on thesecond stage). The window 107 under the first stage now shows that onlythe “4” and the “6” remain as active points.

[0275] The player presses the “Roll Dice” button 102 for the third stageand a possible result is shown in FIG. 31. The roll of 1-1-6 matches oneof the two points that were alive after the second roll. Thus, only thepoint “6” remains alive (107). The point of “4” from the first two rollsis no longer alive because it does not appear in the third roll. Thethree dice are placed on the third stage line 112 next to the paytablevalues for that stage. The game highlights the “1 point matched” valuein the paytable indicating that two coins are awarded for matching onepoint on the third stage. The “Total So Far” meter 110 is updated toshow the total of three coins won at this point (zero coins on the firststage, one coin on the second stage and two coins on the third stage).The window 107 under the first stage now shows that only the “6” remainsas an active point.

[0276] The player presses the “Roll Dice” button 102 for the fourthstage and a possible result is shown in FIG. 32. The roll of 1-4-5 doesnot match the point of “6,” which was the only point left alive. While“4” was an active point after the first two rolls, the absence of a “4”on the third roll took it out of play as a point, and thus was of novalue in the fourth roll. As a result of matching no points the game isover. The “Total So Far” meter 110 value of three coins is copied to the“Paid” window 114, and this is added to the credits counter 115 takingit from an arbitrary “865” to “868” credits.

[0277] It should be noted that in the example shown, the bets for levelsabove the fourth level were lost without those levels being played. Asis intuitive and will be shown in the following analysis, the higher thelevel, the less often it will be played. This is offset by offering theplayer very large awards for very modest events on these higher levelswhen they are played.

[0278] It should also be noted that while the slot machine and pokerembodiments previously discussed have stages that are independent gamesthat allow advancing to the next stage upon winning, this fourth Buncoembodiment is an ongoing game with stages that, as a result of thenature of the game, also involve multi-stage betting working with anevolving game. This game is not limited to advancing to the next stageonly with a win, since the game will always play the second stage if twoor more stages have been bet upon, even though, except for a first stage“Bunco”, the player will not win on the first stage.

[0279]FIG. 33 shows another Bunco game at its conclusion. The first rollof 1-5-5 established only two points as a result of the duplicate 5's.The second roll of 1-3-3 kept only the point of “1” alive. The thirdroll of 1-1-1 is “Bunco” scoring fourteen coins. The fourth roll of3-4-6 does not match the point of “1”, and thus ends the game. A totalof fifteen coins were won on this game (one for matching one point onthe second stage and fourteen for “Bunco” on the third stage).

[0280] Looking at FIG. 33, the “Max Bet/Roll Dice” button 116 is alsoseen. This button 116 establishes the maximum bet, which in thisembodiment is thirty-five coins, (seven stages times five coins perstage) and then rolls the dice for the first stage. Pressing this button116 is the same as pressing the “Select Lines” button 100 until sevenlines are selected, and then pressing the “Coins per Line” button 101until five coins per line are selected, and then finally pressing the“Roll Dice” button 102 to roll the dice for the first stage.

[0281] Shown in the upper right section of FIG. 33 are the bonuses for,games that achieve two “Buncos” and three “Buncos”: “75” coins and“2500” coins respectively. These bonuses add excitement to the game, aswell as the opportunity to win a more sizable award than is availablefrom the seven stages of the game.

[0282] The foregoing Bunco gaming machine is operationally summarized inthe flow charts of FIGS. 34A through 34D. FIG. 34A generally describesthe start-up of the Multi-Strike BUNCO game embodiment, which isinitially quite similar to that of the first (slots) embodiment. First,an assessment of whether credit(s) are present is undertaken beginningat step 460. If none is present, then a check is made as to whether theplayer has inserted the relevant coin, credit card, etc., for thenecessary credit(s) at step 461. If so, then at step 462 the credit(s)are registered and displayed at the “Credits” meter 115 (e.g., FIG. 28).All available player buttons are then activated for initiation of playat 465.

[0283] At this stage, the player enters a set-up loop where the playermay choose to add more credits or proceed with play at step 466. Ifcredits are added, these are registered on the meter display (115) atstep 468. The program loops back to step 466.

[0284] The “Coins per Line” button 101 can alternatively be engaged fromstep 466, causing the coins-per-line setting to be modified (asindicated at meter 103, FIG. 28), as well as updating the value of the“Total Bet” window 104, and the paytable information window 106, all asindicated at step 469. Once again, the program loops back to step 466.

[0285] Back at step 466, the player can choose the “Select Lines” button100 to input this aspect of his or her wager. Graphics are updated atstep 470 to highlight the lines which are now “active” (i.e.,potentially playable). This likewise causes the lines bet meter 111 and“Total Bet” 104 to be so modified, all as indicated at step 472. Theprogram once again loops back to step 466.

[0286] Once the player has input the parameters of the wager, then the“Roll Dice” button 102 is engaged. It should be noted that the foregoingselection sequence as to coins and lines to bet need not follow theorder indicated.

[0287] The player has the option of skipping all of the lines andcoins-per-line selections, through resort to the “Max Bet Roll Dice”button 116 (FIG. 33). A subroutine will then execute at step 475 toassess the total credits the player has provided, and determine themaximum number of coins per line and the maximum number of lines (per anembedded look-up table) which can be played for that credit quantity, upto a fixed maximum for the game. The graphics are updated accordingly atsteps 476 and 477 to show the lines being bet, coins-per-lines and totalbet (as at steps 469, 470 and 472). Either out of step 477 or afteractuation of the “Roll Dice” button 102, the player selection buttonsare deactivated (step 478), the sum of the wager is subtracted from the“Credits” meter 115 and the new amount is displayed. The game thenprogresses to a main play sequence (step 479).

[0288] The dice are rolled at step 480, as shown in FIG. 34B. Theprogram assesses whether this is the first roll of the game (step 482).If it is the first roll, then “Match these POINTS” window 107 (e.g., seeFIG. 29) is activated at step 483, and a determination is made as to howmany different numbers are presented by the rolled dice (step 484). Thedifferent “Points” are then displayed in the window 107, depending onwhether there are one, two or three different numbers (steps 485 athrough 485 c). The graphics of the program generates copies of the dicerolled, with a color hue to indicate a “Point Made” at step 488, and thedice are displayed in the current stage/level/roll (step 489), whichhere is the first level 105.

[0289] If this is not the first roll of the game (step 482), then copiesof the dice just rolled are generated at step 490. The program executesa comparison of the numbers (dice) in the window 107 (which are thePoints to match), with the dice just rolled at step 491. If there is amatch, the graphics of the program colors a copy (or copies) of thematching die rolled with a hue to indicate a “Point Made” at step 492.For each match not made, the die (dice) is colored with a hue toindicate that no match/Point was made (step 493), and the dice aredisplayed as so hued in the current stage/level/roll (step 489).

[0290] From step 489, another comparison is then made at step 495between the current roll and the Point(s) to be matched/made. Each Pointin the window 107 is assessed as to a match on a die (number) of thecurrent roll at step 496. If at step 496 there is no match for a Point,it is removed from the game and the graphics of window 107 are updatedaccordingly, at step 498. The program then assesses whether there is anyPoint remaining (step 497), and the game proceeds to a “Bunco”determination if the answer to the foregoing is positive. If there areno Points remaining (window 107), the player is passed to a “Game Over”sequence at step 500.

[0291] The “Bunco” assessment is set forth in FIG. 34C. The programfirst assesses whether a “Bunco” has been rolled at step 501. If theevaluation is positive, then the graphics highlight the “BUNCO” pay(see, e.g., 113 in FIG. 33) for the current level (step 502). That“BUNCO” pay amount is added to the “Total So Far” meter 110 at step 503.

[0292] The program then determines whether two “Bunco's” had previouslybeen rolled in the same game at step 506. If “yes,” then the “TripleBUNCO BONUS” is highlighted on the screen (step 507), and thepredetermined amount for that bonus is added to the “Total So Far” meter110 at step 508.

[0293] If two “Bunco's” have not been registered at step 506, theprogram makes a determination as to whether one “Bunco” had previouslybeen scored at step 510. If “yes,” then the “Double BUNCO BONUS” ishighlighted on the screen (step 512), and the predetermined amount forthat bonus is added to the “Total So Far” meter 110 at step 513.

[0294] Back at step 501, if a “Bunco” has not been rolled, then a countis made of the number of rolled dice that match any of the remainingPoints in the window 107 (step 515). That count is used to highlight theappropriate pay for that level for that number of points in the paytableinformation window as indicated at step 516. That amount is added to themeter 110 at step 517.

[0295] Out of either step 508, 513 or 517, the player then advances tostep 520, which is a program assessment as to whether all lines thathave been bet on have been played. If all have been played, then thegame is over and the “Game Over” sequence is engaged out of step 521.

[0296] If all possible lines have not been played, then the player isgiven the option of adding more credits and/or continuing throughactuation of the “Roll Dice” button 102 at step 525. If the choice is toadd credits, then the “Credits” meter is so updated at step 526, and theplayer is looped back to step 525. If the choice is to roll, thenanother round is started (step 527) upon actuation of the button 102,whereupon the sequence of events beginning at step 480 recommences.

[0297] Once all lines have been played or there are no Points left inthe window 107 (i.e., no match at a level), then the “Game Over”sequence of FIG. 34D is engaged. A “GAME OVER” message is displayed atstep 530, and a determination is made as to whether the “Total So Far”meter 110 shows any credits (i.e., any winnings for the game) at step531. Any winnings as shown in meter 110 are then added to the total“Credits” meter 115 (step 532), and the player and the program arereturned to the game start sequence at step 460.

[0298] Analysis of Certain Architecture of the Bunco Embodiment

[0299] The mathematical payout percentage of this fourth embodiment isdetermined by breaking down the different possible combinations for eachof the seven stages. This will be done for one coin per line only, as itis well known by those skilled in the art how to expand this result formultiple coins per line, as well as the inclusion of bonus values, ifdesired. The first stage is fairly easy to analyze. There are threepossible types of outcome of the first roll: “Bunco” (equivalent to onepoint established), two points established or three points established.There are two hundred and sixteen possible combinations of three dicecomputed by multiplying the possible combinations of each die:6×6×6=216. The number of occurrences of “Bunco” or three dice that matchare six. This is computed as 6×1×1 because the first die can take any ofthe six numbers, then the second die must match that number and thethird die must also match that number. Three points are established whenall three of the dice have a different number showing, and is computedby 6×5×4=120 because the first die can take on any value while thesecond die can take on any of the five remaining values that don't matchthe first die, and the third die can then take on any of the remainingvalues that don't match the first two dice.

[0300] This leaves ninety occurrences of a combination that results intwo points (216−6−120=90). The ninety occurrences of two points can alsobe computed directly as follows: There are three forms that a rollresulting in two points may take: XYX, XXY or YXX. The combinations forthese are as follows:

[0301] XYX=6×5×1=30 First can be any, second must not match first, thirdmust match first.

[0302] XXY=6×1×5=30 First can be any, second must match first, thirdmust not match first.

[0303] YXX=5×6×1=30 First can be any but X, second can be any, thirdmust match second.

[0304] Table 21 organizes the data described above. The first columnindicates the number of points established by the first roll. The secondcolumn shows the value paid for that result. The third column shows the“Occurrences” of that result which was determined above. The fourthcolumn is the probability of that result, which is the occurrence countdivided by 216, the number of possible outcomes. The fifth column is theExpected Value component from each pay, which is the product of thepaytable value times the probability of receiving that value. The sum ofall EV components is the expected return of the stage, which is 88.89%.If only stage one was played, then the expected return to the playerwould be 88.89%. The payout percentage may be modified by making achange to the second column “Pay” value, which would also change in thepaytable. For example, changing the pay for “Bunco” (one pointestablished) from “32” to “33” would result in a 91.67% expected return.Unlike the slot machine example, the “Occurrence” data is locked intothe rules of the game, and any change to the payout will be apparent tothe player. It must be done by modifying the paytable as describedabove, or by changing the rules of the game. TABLE 21 Number of PointsPay Occurrences Probability EV 1 32   6 0.027777778 0.888889 2 0  900.416666667 0     3 0 120 0.555555556 0     216 1       0.888889

[0305] The second stage of the game has three separate analyses based onthe number of points established in the first stage of the game. The“Occurrences” for each row in Table 22 (the fourth column) arecalculated in the same manner as shown for the first stage and will notbe elaborated on further. The first column of Table 22 states the numberof points alive at the start of the second stage. This table has threeseparate analyses based on whether one, two or three points were aliveat the start of the second stage.

[0306] The second column shows the combination being enumerated. Thethree possible points are called “A”, “B” and “C”. “x” indicates a diethat matches no point. The “Comb. Column” shows the makeup of the dicefor that line of the table. For example, AAA is three dice matchingpoint “A”. The BBA is two dice matching point “B” and one die matchingpoint “A”, and this can occur in any order. The third column indicatesthe amount paid for the specified combination., This is based on thesecond stage paytable line of 1,1,2,6 (e.g., FIG. 30) awarding one coinfor matching one or two points, two coins for matching three points in anon-“Bunco” combination and six coins for all three dice matching thesame point (“Bunco”). The fourth column indicates the number ofoccurrences of the specified combination out of the possible two hundredand sixteen combinations. The fifth column is the probability of thatoccurrence and is the quotient of the occurrences and the two hundredand sixteen possible combinations. The sixth column is called“Probability of Start Condition”. This is the probability of startingthe second stage with the number of points shown in the first column.This number is taken directly from Table 21.

[0307] The seventh column is the probability of the specified “Result”occurring, which is the product of the fifth and sixth columns. Thisresult is due to the need for the probability of the sixth column tostart the stage with the number of points specified in the first column,as well as the need for the probability of the combination, which isgiven in the fifth column.

[0308] The eighth column is the expected value contribution from thiscombination which is computed as the product of the “Pay” value timesthe seventh column “Probability of this Result”. The sum of all valuesin the eighth column provides the expected return which is 92.28%.

[0309] The ninth column is the number of points still alive after theroll. This is represented by the number of unique capitalized letters inthe second column combination.

[0310] The last four columns are used to determine the probability ofthe number of points alive at the end of the stage. The seventh column“Probability of This Result” value is copied to the column thatcorresponds to the ninth column “Points Alive” number. For example, forAAA there is one point alive which results in the 0.00013 value to becopied from the seventh column to the eleventh column, which is thecolumn that calculates the “Probability that Points Left=1”.

[0311] The bolded numbers at the bottom of the last four columns ofTable 22 tally the probability of ending the second round with thenumber of Points specified at the head of the column. For example, ofthe games that play a second stage (which is all games in thisembodiment), 24.31% will finish the second stage with two points active.TABLE 22 Points Alive Points Prob. Prob. Prob. Prob. at ProbabilityProb. Of Alive That That That That Round Probability of of Start ThisAfter Points Points Points Points Start Comb. Pay Occur. OccurrenceCondition Result EV Roll Left = 0 Left = 1 Left = 2 Left = 3 1 AAA 6  10.00462963 0.02777778 0.000129 0.000772 1 0.00013 1 AAx 1  15 0.069444440.02777778 0.001929 0.001929 1 0.00193 1 Axx 1  75 0.34722222 0.027777780.009645 0.009645 1 0.00965 1 xxx 0 125 0.5787037 0.02777778 0.016075 00 0.01608 216 1 2 AAA 6  1 0.00462963 0.41666667 0.001929 0.011574 10.00193 2 BBB 6  1 0.00462963 0.41666667 0.001929 0.011574 1 0.00193 2AAB 2  3 0.01388889 0.41666667 0.005787 0.011574 2 0.00579 2 BBA 2  30.01388889 0.41666667 0.005787 0.011574 2 0.00579 2 AAx 1  12 0.055555560.41666667 0.023148 0.023148 1 0.02315 2 BBx 1  12 0.05555556 0.416666670.023148 0.023148 1 0.02315 2 ABx 1  24 0.11111111 0.41666667 0.0462960.046296 2 0.0463 2 Axx 1  48 0.22222222 0.41666667 0.092593 0.092593 10.09259 2 Bxx 1  48 0.22222222 0.41666667 0.092593 0.092593 1 0.09259 2xxx 0  64 0.2962963 0.41666667 0.123457 0 0 0.12346 216 1 3 AAA 6  10.00462963 0.55555556 0.002572 0.015432 1 0.00257 3 BBB 6  1 0.004629630.55555556 0.002572 0.015432 1 0.00257 3 CCC 6  1 0.00462963 0.555555560.002572 0.015432 1 0.00257 3 AAB 2  3 0.01388889 0.55555556 0.0077160.015432 2 0.00772 3 AAC 2  3 0.01388889 0.55555556 0.007716 0.015432 20.00772 3 BBA 2  3 0.01388889 0.55555556 0.007716 0.015432 2 0.00772 3BBC 2  3 0.01388889 0.55555556 0.007716 0.015432 2 0.00772 3 CCA 2  30.01388889 0.55555556 0.007716 0.015432 2 0.00772 3 CCB 2  3 0.013888890.55555556 0.007716 0.015432 2 0.00772 3 ABC 2  6 0.02777778 0.555555560.015432 0.030864 3 0.01543 3 ABx 1  18 0.08333333 0.55555556 0.0462960.046296 2 0.0463 3 ACx 1  18 0.08333333 0.55555556 .0.046296 0.046296 20.0463 3 BCx 1  18 0.08333333 0.55555556 0.046296 0.046296 2 0.0463 3AAx 1  9 0.04166667 0.55555556 0.023148 0.023148 1 0.02315 3 BBx 1  90.04166667 0.55555556 0.023148 0.023148 1 0.02315 3 CCx 1  9 0.041666670.55555556 0.023148 0.023148 1 0.02315 3 Axx 1  27 0.125 0.555555560.069444 0.069444 1 0.06944 3 Bxx 1  27 0.125 0.55555556 0.0694440.069444 1 0.06944 3 Cxx 1  27 0.125 0.55555556 0.069444 0.069444 10.06944 3 xxx 0  27 0.125 0.55555556 0.069444 0 0 0.06944 216 1 EV ofsecond Stage: 0.92284 Prob. Of Start Cond. For 0.20898 0.53254 0.243060.01543 Next Stage Total of 4 probability 1 values above

[0312] Table 23 provides a similar analysis for the third stage of thegame. The first two columns are the same. The third column has beenmodified to reflect the 2-2-5-14 (e.g., FIG. 31) paytable values for thethird stage. The fourth column is the same as Table 22.

[0313] The fifth column uses the “Probability of Start Condition” forthe specified number of points taken from the bottom of Table 22. Thosenumbers at the bottom of Table 22 show the probability of ending thesecond stage with zero, one, two or three points. The values in the restof the columns are calculated in the same manner as was described forTable 22.

[0314] Looking at the sum of the “EV” column, it is clear that theexpected return for the third stage of the game is 90.24%. The rightfour columns are used to compute the probability of zero, one, two orthree points remain alive after the third stage. Note that the sum ofthese probability values does not total 1.0, but rather 0.79102. Theadditional component is the 0.20898 found at the bottom of Table 22under “Probability that Points Left=0”. This represents games that endedafter two stages and thus are not reflected in the stage three endingbreakdown. In the same manner, the 0.3821 probability of ending the gamein the third stage will not be included in the stage four endingbreakdown.

[0315] The analysis for stages four through seven is done in a manneridentical to stage three. The comparable tables for these stages aretherefore not shown. TABLE 23 Points Alive Points Prob. Prob. Prob.Prob. at Probability Prob. Of Alive That That That That RoundProbability of of Start This After Points Points Points Points StartComb. Pay Occur. Occurrence Condition Result EV Roll Left = 0 Left = 1Left = 2 Left = 3 1 AAA 14  1 0.00462963 0.532536 0.0024654 0.0345162 10.0025 1 AAx  2  15 0.06944444 0.532536 0.0369817 0.0739633 1 0.037 1Axx  2  75 0.34722222 0.532536 0.1849083 0.3698167 1 0.1849 1 xxx  0 1250.5787037 0.532536 0.3081806 0 0 0.3082 216 1 2 AAA 14  1 0.004629630.2430556 0.0011253 0.0157536 1 0.0011 2 BBB 14  1 0.00462963 0.24305560.0011253 0.0157536 1 0.0011 2 AAB  5  3 0.01388889 0.2430556 0.00337580.0168789 2 0.0034 2 BBA  5  3 0.01388889 0.2430556 0.0033758 0.01687892 0.0034 2 AAx  2  12 0.05555556 0.2430556 0.0135031 0.0270062 1 0.01352 BBx  2  12 0.05555556 0.2430556 0.0135031 0.0270082 1 0.0135 2 ABx  2 24 0.11111111 0.2430556 0.0270062 0.0540123 2 0.027 2 Axx  2  480.22222222 0.2430556 0.0540123 0.1080247 1 0.054 2 Bxx  2  48 0.222222220.2430556 0.0540123 0.1080247 1 0.054 2 xxx  0  64 0.2962963 0.24305560.0720165 0 0 0.072 216 1 3 AAA 14  1 0.00462963 0.0154321 7.144E−050.0010002 1 7E−05 3 BBB 14  1 0.00462963 0.0154321 7.144E−05 0.0010002 17E−05 3 CCC 14  1 0.00462963 0.0154321 7.144E−05 0.0010002 1 7E−05 3 AAB 5  3 0.01388889 0.0154321 0.0002143 0.0010717 2 0.0002 3 AAC  5  30.01388889 0.0154321 0.0002143 0.0010717 2 0.0002 3 BBA  5  3 0.013888890.0154321 0.0002143 0.0010717 2 0.0002 3 BBC  5  3 0.01388889 0.01543210.0002143 0.0010717 2 0.0002 3 CCA  5  3 0.01388889 0.0154321 0.00021430.0010717 2 0.0002 3 CCB  5  3 0.01388889 0.0154321 0.0002143 0.00107172 0.0002 3 ABC  5  6 0.02777778 0.0154321 0.0004287 0.0021433 3 0.000433 ABx  2  18 0.08333333 0.0154321 0.001286 0.002572 2 0.0013 3 ACx  2 18 0.08333333 0.0154321 0.001286 0.002572 2 0.0013 3 BCx  2  180.08333333 0.0154321 0.001286 0.002572 2 0.0013 3 AAx  2  9 0.041666670.0154321 0.000643 0.001286 1 0.0006 3 BBx  2  9 0.04166667 0.01543210.000643 0.001286 1 0.0006 3 CCx  2  9 0.04166667 0.0154321 0.0006430.001286 1 0.0006 3 Axx  2  27 0.125 0.0154321 0.001929 0.003858 10.0019 3 Bxx  2  27 0.125 0.0154321 0.001929 0.003858 1 0.0019 3 Cxx  2 27 0.125 0.0154321 0.001929 0.003858 1 0.0019 3 xxx  0  27 0.1250.0154321 0.001929 0 0 0.0019 216 1 EV of third Stage: 0.9023574 Prob.Of Start Cond. For Next Stage 0.3821 0.3696 0.0389 0.00043 Total of 4probability values above 0.79102

[0316] The analysis provided thus far does not include the bonuses fortwo “Buncos” and three “Buncos” occurring in the same game. Theprobability of getting a second or third “Bunco” in a game must beanalyzed on a stage by stage basis, with the expected value of suchawards added to the EV of the stage in which the bonus occurs.

[0317] A double “Bunco” award is given on a particular stage when thesecond “Bunco” in a game is achieved in that stage. It is not possibleto get a double “Bunco” in the first stage. In the second stage, theonly way to achieve a double “Bunco” bonus is to roll a “Bunco” on eachof the first two stages. On the third stage, one could get “Bunco” onthe first and third stage, or the second and third stage (the first andsecond stage is the case noted above of getting a double “Bunco” on thesecond stage). The shorthand xBB is used to indicate no “Bunco” on thefirst stage followed by “Bunco” on the second and third stages, whilesimilarly BxB indicates “Bunco” on the first and third stages with no“Bunco” on the second stage.

[0318] Table 24 shows the combinations that will result in a double“Bunco” on the seventh stage. Note that all combinations must have thesecond “Bunco” occur as the seventh stage because if the second “Bunco”occurred earlier then it would be attributed to the earlier stage.

[0319] BxxxxxB

[0320] xBxxxxB

[0321] xxBxxxB

[0322] xxxBxxB

[0323] xxxxBxB

[0324] xxxxxBB

[0325] Table 24

[0326] Working through the cases in Table 24, it is found that as aresult of symmetry, the probability of each of these components to aseventh level double “Bunco” is identical. Likewise, there are five waysof identical probability to achieve a sixth level double “Bunco” bonusand the two ways mentioned above to achieve a third level double “Bunco”bonus have identical probability.

[0327] In order to compute the probability of the required components,there is a need to use three values that were computed earlier. In Table21, the probability of a “Bunco” on the first roll is shown to be0.027777778. The “x” components in the first line of Table 24 is theprobability of staying alive in a game that has established one point,by rolling anything but a “Bunco”. This is found by taking the secondand third lines of Table 22 (AAx and Axx) and adding the probability ofthose rolls (fourth column), which results in a total of 0.416666667.Finally, there is the probability of rolling a “Bunco” while one pointis alive. This is shown in the first line of Table 22 (AAA) as0.00462963. Using these values, one may construct the double “Bunco”probability table of Table 25.

[0328] The first column of Table 25 shows the game “Stage” for which theprobability of double “Bunco” is being computed. The second column isthe “Number of Forms” a double “Bunco” may take on that stage (such asthe six forms shown for the seventh stage in Table 24). The third columnshows the “Sample Form” being computed for the stage. The fourth throughtenth columns are the probability components matching the respectiveletters in the third column forms. The eleventh column is the“Probability” of getting a double “Bunco” on that level which is theproduct of the second column form count and all probability components(“Comp.” 1 through 7). TABLE 25 Double Number Sample Bunco Stage ofForms Form Comp. 1 Comp. 2 Comp. 3 Comp. 4 Comp. 5 Comp. 6 Comp. 7Probability 1 0 0 2 1 BB 0.027778 0.00463 0.000128601 3 2 BxB 0.0277780.416667 0.00463 0.000107167 4 3 BxxB 0.027778 0.416667 0.416667 0.004636.69796E−05 5 4 BxxxB 0.027778 0.416667 0.416667 0.416667 0.004633.72109E−05 6 5 BxxxxB 0.027778 0.416667 0.416667 0.416667 0.4166670.00463 1.93807E−05 7 6 BxxxxxB 0.027778 0.416667 0.416667 0.4166670.416667 0.416667 0.00463 9.69033E−06

[0329] The analysis for the “Triple Bunco Bonus” is similar to the“Double Bunco Bonus.” Table 26 shows all of the possible forms of aseventh level “Triple Bunco Bonus.” TABLE 26 BBxxxxB BxBxxxB BxxBxxBBxxxBxB BxxxxBB xBBxxxB xBxBxxB xBxxBxB xBxxxBB xxBBxxB xxBxBxB xxBxxBBxxxBBxB xxxBxBB xxxxBBB

[0330] Using the same symmetry that was used for the double “Bunco”calculation, one arrives at Table 27. TABLE 27 Number Triple of SampleBunco Stage Forms Form Comp. 1 Comp. 2 Comp. 3 Comp. 4 Comp. 5 Comp. 6Comp. 7 Probability 1 0 0 2 0 0 3 1 BBB 0.027778 0.00463 0.004635.95374E−07 4 3 BBxB 0.027778 0.00463 0.416667 0.00463 7.44218E−07 5 6BBxxB 0.027778 0.00463 0.416667 0.416667 0.00463 6.20181E−07 6 10 BBxxxB0.027778 0.00463 0.416667 0.416667 0.416667 0.00463 4.30682E−07 7 15BBxxxxB 0.027778 0.00463 0.416667 0.416667 0.416667 0.416667 0.004632.69176E−07

[0331] Table 28 shows the expected return from the double “Bunco” andtriple “Bunco” awards. The first column shows the game “Stage”. Thesecond column shows the “75” coin pay for the “Double Bunco Bonus”. Thethird column shows the “Double Bunco Probability” computed in Table 25for each stage. The fourth column computes the expected return” (EV) fordouble “Buncos” on the given stage by multiplying the “Pay” (secondcolumn) times the “Probability” (third column). The fifth throughseventh columns compute the triple “Bunco” expected return in the samemanner as was used for “Double Bunco” in the second through fourthcolumns. TABLE 28 Double Double Double Triple Triple Triple Bunco BuncoBunco Bunco Bunco Bunco Stage Pay Prob. EV Pay Prob. EV 1 75 0 0 2500 00 2 75 0.000129 0.009645 2500 0 0 3 75 0.000107 0.008038 2500 5.95E−070.001488 4 75  6.7E−05 0.005023 2500 7.44E−07 0.001861 5 75 3.72E−050.002791 2500  6.2E−07 0.00155 6 75 1.94E−05 0.001454 2500 4.31E−070.001077 7 75 9.69E−06 0.000727 2500 2.69E−07 0.000673

[0332] Finally, the overall EV of each stage and the overall EV ofmulti-stage games is shown in Table 29. The first column indicates the“Stage” number. The second column shows the expected return for the basegame stage which was generated for the first three stages in Table 21,Table 22, and Table 23. The third and fourth column show the “Double”and “Triple Bunco” bonus EV components generated in Table 28. The fifthcolumn is the total EV for the stage, which is created by adding the EVcomponents in the second, third and fourth columns. The sixth column isthe EV of an entire multi-stage game that bet on the number of stages inthe first column. This is the average of the fifth column in the currentrow and all rows above (i.e., the average EV of all stages in themulti-stage game). The expected return of the entire game when a playerplays all seven stages is 0.927423292 or 92.74%. Base Double Triple EVof Game Game Bunco Bunco Total EV Playing this Stage EV EV EV For Stagemany stages 1 0.888889 0 0 0.888889 0.888888889 2 0.92284 0.009645 00.932485 0.910686728 3 0.902357 0.008038 0.001488 0.911883 0.911085629 40.921469 0.005023 0.001861 0.928353 0.915402545 5 0.953178 0.0027910.00155 0.957519 0.923825811 6 0.937292 0.001454 0.001077 0.9398220.92649184 7 0.931612 0.000727 0.000673 0.933012 0.927423292

[0333] It will additionally be noted that the invention furthercontemplates a training program for players of these games, particularlyin the video game versions. Such training programs are designed to teachplayers not only the fundamentals of game play, but to optimize gameplaying strategy, as with visual and aural cues for the player, replayoptions, and the like. Representative training programs are disclosed inapplicants' co-pending patent application Ser. No. 09/539,286, filedMar. 30, 2000, and that disclosure is hereby incorporated by reference.

[0334] Thus, while the invention has been disclosed and described withrespect to certain embodiments, those of skill in the art will recognizemodifications, changes, other applications and the like which willnonetheless fall within the spirit and ambit of the invention, and thefollowing claims are intended to capture such variations.

What is claimed is:
 1. A method of playing a wagering game having anumber of stages to be wagered on, comprising: a player making a wageraccording to a number of sequential stages desired to be played;initiating play of a first stage of the game, wherein if a win isexperienced on the first stage and if the second stage was wagered, playof the game advances to the second stage and a payout is earned, andwherein if a win is not experienced, the game is over and all wagers arelost; initiating play of a second stage of the game, wherein if a win isexperienced on the second stage and if the third stage was wagered, playof the game advances to a third stage and a payout is earned, wherein ifa win on the second stage is not experienced, the game is over and allwagers, except the payout on the first stage win, are lost; sequentiallyinitiating play of any number of respective stages of the game after thesecond stage, the any number of stages comprising one of a final stagewhich is a pre-set maximum stage for the game, and a desired stage, thedesired stage being a stage between the final and the second stageoptionally selected by the player to be the utmost wagered stage,wherein if a win is sequentially experienced on each sequentiallysucceeding stage up to and including one of the final and desired stage,and if each succeeding stage up to and including the one of the finaland desired stage was wagered, then a payout is earned on eachsequential stage and play of the game advances sequentially up to andincluding one of the final and desired stage, wherein after the play ofone of the final and desired stage, the game is then over, and whereinif a win is not experienced on any played stage after the first stage,the game is over and all wagers, except the payouts from any of thepreceding stages, are lost.
 2. The method of claim 1, wherein the gameis a slots game, and each stage is a slot machine device having one ormore betting lines.
 3. The method of claim 2, wherein the game has atleast three stages.
 4. The method of claim 3, wherein each stage usesthe same paytable, and each stage has a respective payout multiplier,each stage multiplier being different from another stage multiplier andincreasing with successive stages.
 5. The method of claim 4, wherein afinal stage multiplier is based upon a random number generator.
 6. Themethod of claim 1 wherein a win comprises a net positive result of apayout for a given stage relative to a respective wager for that stage.7. The method of claim 1, wherein the game is comprised of a multi-stage“Five-Card Stud” poker game, the game having at least three stages, eachstage having a respective poker betting hand.
 8. The method of claim 7,wherein a win includes a “Free Ride” feature, wherein the game willautomatically advance a player from a current stage to a succeedingstage, independently of whether the current stage includes a winninghand, if the “Free Ride” feature is dealt in the current stage.
 9. Themethod of claim 8, wherein one paytable is used for the game, and eachstage has a respective payout multiplier, each stage multiplier beingdifferent from another stage multiplier and increasing with successivestages.
 10. The method of claim 1, wherein the game is comprised of a“Five-Card Draw” poker game.
 11. The method of claim 10, furthercomprising dealing at each stage a hand of at least five cards, all faceup, in a first deal; selecting none, one, or more than one of the faceup cards as cards to be held; discarding from the first deal thenon-held cards and replacing those cards with a face-up card to arriveat a resultant five cards; determining a poker hand ranking of theresultant cards of the hand.
 12. The method of claim 11, wherein eachstage uses the same paytable, and each stage has a respective payoutmultiplier, each stage multiplier being different from another stagemultiplier and increasing with successive stages.
 13. A method ofplaying a wagering dice game having a plurality of stages to be wageredagainst, each stage representing a roll of the dice, comprising: aplayer making a wager according to a number of stages desired to beplayed, wherein the wager made on a stage creates an eligibility forplaying that stage; initiating play of a first stage of the game byrolling plural dice, wherein each different number appearing on each ofthe die becomes a respective point-to-match that is stored anddisplayed, wherein if all die numbers match, a win is experienced and apayout is earned, and wherein play advances to a second stage if thesecond stage was wagered, independent of whether a win was experienced;initiating play of a second stage by rolling the dice; determiningwhether any of the numbers appearing on a die from the second roll matchthe point(s)-to-match, wherein at least one match is considered a winand play advances to a third stage if the third stage was wagered, butthe game is over and any remaining wagers are lost if there is no match,and further wherein for a point matched, a payout is earned, eachpoint-to-match that matches at least one of the dice for the secondstage remaining for a third stage, if a third stage was wagered upon;initiating play of a third stage by rolling the dice; determiningwhether any numbers appearing on a die from the third roll match thepoint(s)-to-match left from the second stage, wherein at least one matchis considered a win and play advances to a fourth stage if the fourthstage was wagered, but the game is over and any remaining wagers arelost if there is no match, and further wherein for a point matched,another payout is earned, each point-to-match that matches at least oneof the dice for the third stage remaining for a fourth stage if a fourthstage was wagered upon; initiating play of a fourth through n^(th) stageby rolling the dice in each respective stage; and making an identicaldetermination for each respective fourth through n^(th) stage asperformed for the second and third stages in order to continue play upto the n^(th) stage, or to end the game when no point(s)-to-matchremaining from a preceding stage can be matched to the numbers appearingon the dice of a current stage.
 14. The method of claim 13, wherein a“Bunco” bonus is awarded when a roll of the dice results with allnumbers of the dice matching and further matching a point-to-match. 15.A video machine configured as a wagering game, comprising: a first, asecond, and up to predetermined n^(th) stage to be wagered upon; aninput for wagering an amount; a microprocessor receiving signals fromthe input for determining the number of stages to be wagered, andincluding a program for controlling the play of the game as a functionof the stages wagered wherein, a player makes a wager according to anumber of stages desired to be played; play of a first stage of the gameis initiated, and if a win is experienced on the first stage and if thesecond stage was wagered, play of the game advances to the second stage,a payout is earned, but if a win is not experienced, the game is overand all wagers are lost; play of a second stage of the game is initiatedif wagered and the first stage resulted in a win, and if a win isexperienced on the second stage and the next successive stage waswagered, play of the game advances to the succeeding stage, a payout isearned, but if a win on the second stage is not experienced, the game isover and all wagers, except the payout on the first stage win, are lost;play of each successive stage up to the n^(th) stage of the game isinitiated, and if a win is experienced on each successive stage, apayout is earned and the game continues to a subsequent stage, but if awin is not experienced, the game is over and only payouts from thepreceding stages are retained.
 16. The machine of claim 15, wherein thegame is a multi-stage slot machine.
 17. The machine of claim 15, whereinthe game is “Five Card Stud” poker.
 18. The machine of claim 15, whereinthe game is “Draw” poker.
 19. The machine of claim 15, wherein the gameis a dice game.
 20. A method of playing a game, comprising the steps of:(a) providing a player with a first stage game of chance upon which afirst wager is placed by the player; (b) providing the player with asecond stage game of chance upon which a second wager is placeable; eachsaid stage having an advancement condition and a terminating condition;(c) playing said first stage game; (d) determining which of saidadvancement and terminating conditions is presented by said first stagegame as played; (e) if an advancement condition is presented by saidfirst stage game as played, then advancing to said second stage game,but if a terminating condition is presented by said first stage game asplayed, the game is over and at least part of said second wager is lost;(f) playing said second stage game if an advancement condition ispresented at step (e) and a second wager has been placed; and (g)determining which of said advancement and terminating conditions ispresented by said second stage game as played.
 21. The method of playinga game of claim 20 further including the step of providing a payout foran advancement condition at the second stage.
 22. The method of playinga game of claim 21 further including the step of providing a payout foran advancement condition at each stage.
 23. The method of playing a gameof claim 22 wherein said payout is based upon the amount of a respectivewager at a respective stage.
 24. The method of playing a game of claim23 wherein said payout is increased by a multiplier for a respectivestage.
 25. The method of playing a game of claim 24 wherein saidmultiplier increases for each successive stage.
 26. The method ofplaying a game of claim 20 wherein said first and second games of chanceare the same type of game.
 27. The method of playing a game of claim 26wherein said type of game is a slot machine device.
 28. The method ofplaying a game of claim 27 wherein said slot machine device is a videoslot machine having visual representations of plural slot reels.
 29. Themethod of playing a game of claim 26 wherein said type of game is a cardgame.
 30. The method of playing a game of claim 29 wherein said cardgame is selected from one of “Draw” and “Stud” poker.
 31. The method ofplaying a game of claim 26 wherein said type of game is a dice game. 32.The method of playing a game of claim 20 wherein said first and secondgames of chance are different types of games.
 33. A method of playing agame, comprising the steps of: (a) providing a player with a first stagegame of chance upon which a first wager is placed by the player; (b)providing the player with a successive stage game of chance (n₁) up to apredetermined n^(th) stage (n_(x)) game of chance upon which respectiven₁ to n_(x) wagers are placeable; each said stage having a winningcondition and a losing condition; (d) playing said first stage game; (e)determining which of said winning and losing conditions is presented bysaid first stage game as played; (f) if a winning condition is presentedby said first stage game as played, then advancing to said successivestage game, but if a losing condition is presented by said first stagegame as played, the game is over and any wager at a stage higher thanthe first game stage is lost; (g) playing said successive stage game ifa winning condition is presented by said first stage game as played, anda wager has been placed on said successive stage game; (h) determiningwhich of said winning and losing conditions is presented by saidsuccessive stage game as played, and if a winning condition ispresented, then advancing through additional stage games up through saidn^(th) stage game if at each respective additional stage game a wagerhas been placed on that stage game and its preceding stage game presentsa winning condition, but if a losing condition is presented at anadditional stage game, the game is over and any wager at a stage higheris lost.
 34. The method of playing a game of claim 33 further includingthe step of providing a payout for a winning condition at each stage.35. The method of playing a game of claim 34 wherein said payout isbased upon the amount of a respective wager at a respective stage, saidpayout is increased by a multiplier for a respective stage, and saidmultiplier increases at each stage reached.
 36. A method for operating aprocessor-controlled gaming machine comprising the steps of: (a)providing gameplay elements in a manner that can be visualized by aplayer; (b) providing a mechanism for a wager input from the player; (c)providing a mechanism for game operational input from the player; (d)providing a first stage game of chance upon which a first wager isplaced by the player; (e) providing the player with a second stage gameof chance upon which a second wager is placeable; each said stage havingan advancement condition and a terminating condition; (f) displaying atleast said first stage game using at least some of said gameplayelements; (g) playing said first stage game; (h) determining which ofsaid advancement and terminating conditions is presented by said firststage game as played; (i) if an advancement condition is presented bysaid first stage game as played, then advancing to said second stagegame, but if a terminating condition is presented by said first stagegame as played, the game is over and at least part of said second wageris lost; (j) displaying said second stage game of chance using at leastsome of said gameplay elements if said second stage game is not alreadydisplayed and playing said second stage game if an advancement conditionis presented at step (i) and a second wager has been placed; (k)determining which of said advancement and terminating conditions ispresented by said second stage game as played; and (l) providing apayout for an advancement condition.
 37. The method of claim 36 furtherincluding the step of providing a payout for an advancement condition ateach stage.
 38. The method of claim 36 further including the steps of:(m) providing the player with a third stage game of chance and up to ann^(th) stage game of chance upon which a third wager and up to an n^(th)wager are respectively placeable; (n) displaying said third stage gameof chance using at least some of said gameplay elements if said thirdstage game is not already displayed and playing said third stage game ifan advancement condition is presented at step (k) and a third wager hasbeen placed; (o) determining which of said advancement and terminatingconditions is presented by said third stage game as played; and (p)displaying if not already displayed, using at least some of saidgameplay elements, and playing seriatim each successive stage after saidthird stage game up to said n^(th) stage game, if said third stage gameand successive stages thereafter respectively present an advancementcondition and a successive respective wager has been placed.
 39. Themethod of claim 38 wherein said payout is based upon the amount of wagerat a respective stage, and said payout is increased by a multiplier fora respective stage, with said multiplier increasing as at least somestages are reached.
 40. The method of claim 38 wherein said gameplayelements comprise a slot machine device having visual representations ofplural slot reels.
 41. The method of claim 40 wherein a separate slotmachine device is visually displayed for each stage, with a plurality ofstages being displayed together on a visual display.
 42. The method ofclaim 38 wherein said gameplay elements are cards for a card game ofchance.
 43. The method of claim 42 wherein a hand of cards is visuallydisplayed for each stage, with a plurality of stages being displayedtogether on a visual display.
 44. The method of claim 38 wherein saidgameplay elements are dice.
 45. The method of claim 44 further includingthe steps of: providing a set of differing gameplay element indicia, andestablishing from said set of gameplay element indicia a subset of atleast one match indicia against which said dice are to be matched in thecourse of play, said dice having a plurality of said gameplay elementindicia represented thereon as facets of each die; displaying saidfirst, second, third and successive stages up to said n^(th) stagetogether as discrete arrays on a visual display; tossing said dice andbeginning with at least said second stage game, determining any matchbetween said match indicia and said die indicia, with at least one matchcomprising an advancement condition for a stage being played; andremoving from further play any match indicium which is not matched at astage.
 46. The method of claim 45 further including the steps of:providing a visual representation of said die indicia resulting from arespective toss on a respective array of said visual display; andproviding a visual representation of each said match indicia remainingin play.
 47. The method of claim 38 wherein said payout is based upon atable which increases the amount of payout for a given wager as at leastsome stages are reached.
 48. The method of claim 38 further includingthe step of: providing a feature which is subject to random allocationto a stage in the course of play, said feature if allocated constitutingan advancement condition enabling a next stage to be played, provided awager has been placed on said next stage which is subject to being soenabled for play.
 49. A video card game comprising: a video displaydevice; a cpu having a program; a wager input mechanism which registersa wager placed by a player, said wager including an ability to registerbets upon successive stages of the game; a first deck of playing cardscomprised of cards of suit and rank generated by said program, saidprogram establishing a first array for display of a subset of said deck,said subset comprising a hand of cards randomly selected from said deck;said program dealing a first stage hand of cards, and determiningwhether said hand of cards presents a winning condition based upon apreset hierarchical ranking of card arrangements relating to suit andrank; said program dealing a second stage hand of cards provided a bethas been registered for said second stage and a winning condition ispresented by said first stage hand as played, but if a losing conditionis presented by said first stage hand as played, the game is over and atleast a portion of bets on said first and second stage hands are lost;said program including a payout output based upon said wager andpredetermined values for said first and second stage hands according toa preset hierarchical ranking of card arrangements relating to suit andrank.
 50. The video game of claim 49 further comprising a second deck ofplaying cards from which said second stage hand of cards is dealt andsuccessive decks of playing cards for a respective successive stage handof cards, and wherein said program deals a successive stage hand ofcards provided a bet has been registered for a respective successivestage hand of cards and a winning condition is presented by a nextpreceding stage hand as played, up to a predetermined n^(th) stage. 51.The video game of claim 50 wherein said payout output includes a payoutfor a bet on any stage hand of cards presenting a winning condition asplayed.
 52. The video game of claim 51 wherein said payout outputincludes payout tables which are different for at least some of saidstages.
 53. The video game of claim 51 wherein said payout outputincludes a payout table which is the same for each stage, but includes amultiplier for at least some of said stages, said multiplier increasingfor successively higher stages.
 54. The video game of claim 51 furtherincluding a feature generated by said program which is subject to randomallocation to a stage in the course of play, said feature if allocatedconstituting a winning condition enabling said second and any successivestage to be played regardless of a winning condition otherwise beingpresented at said first, second and a next preceding stage,respectively, provided a bet has been placed on said respective second,successive and next successive stage, respectively, which is subject tobeing so enabled for play.
 55. The video game of claim 50 wherein saidfirst stage hand of cards is visually displayed in said first array, asecond array is provided for display of said second stage hand of cards,and successive arrays are provided for display of respective successivestage hands of cards, with a plurality of arrays being displayedtogether on said visual display.
 56. The video game of claim 55 whereinthe card game is “Draw” poker, and said game further includes amechanism for inputting player command selections for indicating one ormore cards to be held in a hand being played, said program dealing cardsfrom those remaining in a respective deck to replace any card not heldto complete play of a stage hand of cards.
 57. A video slot machinecomprising: a video display device; a cpu having a program operating aslots game; a wager input mechanism which registers a wager placed by aplayer, said wager including an ability to register bets upon successivestages of play of the machine; a plurality of rotatable reels generatedby said program, each of said reels being comprised of a plurality ofdifferent indicia, wherein each of said reels is caused by said programto appear to rotate and then randomly stop to thereby yield a display ofcertain indicia as a spin of said reels; said program establishing afirst stage spin, and determining whether said first stage spin presentsa winning condition based upon a preset ranking of various indiciaarrangements; said program establishing a second stage spin if a bet hasbeen registered for said second stage spin and a winning condition ispresented by said first stage spin, but if a losing condition ispresented by said first stage spin, the game is over and at least aportion of bets on said first and second stage spins are lost; saidprogram including a payout output based upon said wager andpredetermined values for said first and second stage spins according tosaid preset ranking.
 58. The slot machine of claim 57 wherein saidprogram establishes a successive stage spin provided a bet has beenregistered for a respective successive stage spin and a winningcondition is presented by a next preceding stage spin, up to apredetermined n^(th) stage spin.
 59. The slot machine of claim 58wherein said payout output includes a payout for a bet on any stage spinpresenting a winning condition, and said payout output includes a payouttable which is the same for each stage spin, but includes a multiplierfor at least some of said stages, said multiplier increasing forsuccessively higher stages.
 60. The slot machine of claim 58 furtherincluding a feature generated by said program which is subject to randomallocation to a stage in the course of play, said feature if allocatedconstituting a winning condition enabling said second and any successivestage to be played regardless of a winning condition being presented ata next preceding stage, provided a bet has been placed on said nextsuccessive stage which is subject to being so enabled for play.
 61. Theslot machine of claim 58 wherein said first stage spin is visuallydisplayed as a first set of reels in a first array, said second stagespin is visually displayed as a second set of reels in a second array,and successive stage spins are each displayed as further sets of reelsin successive respective arrays, with a plurality of arrays beingdisplayed together on said visual display.
 62. The slot machine of claim59 wherein said multiplier for said n^(th) stage spin is randomlyselected by said program from a predetermined table of multipliers, atleast most of said multipliers being greater than a multiplier for asuccessive stage spin next preceding said n^(th) stage spin.
 63. Theslot machine of claim 62 wherein selection of said multiplier for saidn^(th) stage is displayed by said program as a wheel having segmentswith said predetermined multipliers displayed in respective segments ofsaid wheel, and said wheel is caused to appear to rotate and come to astop with said random multiplier at a designated stop point.
 64. Thevideo game of claim 53 wherein said multiplier for said n^(th) stage israndomly selected by said program from a predetermined table ofmultipliers, at least most of said multipliers being greater than amultiplier for a successive stage next preceding said n^(th) stage. 65.The video game of claim 64 wherein selection of said multiplier for saidn^(th) stage is displayed by said program as a wheel having segmentswith said predetermined multipliers displayed in respective segments,and said wheel is caused to appear to rotate and come to a stop withsaid random multiplier at a designated stop point.
 66. A slot machinecomprising: a wager input mechanism which registers a wager placed by aplayer, said wager input mechanism including a register of bets uponsuccessive stages of play of the machine; a plurality of rotatablereels, each of said reels having a plurality of different indiciathereon, wherein each of said reels is caused by a spin device to rotateand then randomly stop to thereby yield a display of certain indicia asa spin of said reels; a spin mechanism actuated by a player to causesaid spin device to operate; a control apparatus which senses restpositions of said indicia on a spin and determines whether a spinpresents an advancement condition based upon a preset ranking of variousindicia arrangements used by said control apparatus; said controlapparatus permitting at least a first stage spin upon registration of awager and actuation of said spin mechanism, and permitting a secondstage spin if a bet has been registered for said second stage spin andan advancement condition is determined for said first stage spin, but ifan advancement condition is not determined for said first stage spin,the game is terminated and at least a portion of bets on said first andsecond stage spins are lost; a payout device yielding a payout accordingto said preset ranking.
 67. The slot machine of claim 66 wherein saidcontrol apparatus establishes a successive stage spin provided a bet hasbeen registered for a respective successive stage spin and a winningcondition is determined for a next preceding stage spin, up to apredetermined n^(th) stage spin.
 68. The slot machine of claim 67wherein said payout device includes a payout table which is the same foreach stage spin with a multiplier for at least some of said stages, saidmultiplier increasing for successively higher stages.
 69. The slotmachine of claim 67 wherein a first plurality of reels is used for saidfirst stage spin, a second plurality of reels is used for said secondstage spin, and successive pluralities of reels are used for eachsuccessive stage spin.
 70. The slot machine of claim 68 wherein saidmultiplier for said n^(th) stage spin is randomly selected by saidcontrol apparatus from a predetermined table of multipliers, at leastmost of said multipliers being greater than a multiplier for asuccessive stage spin next preceding said n^(th) stage spin.
 71. Theslot machine of claim 70 wherein selection of said multiplier for saidn^(th) stage is effected by spinning a wheel having said predeterminedmultipliers displayed in respective segments, said wheel coming to astop with said random multiplier at a designated stop point sensed bysaid control apparatus.
 72. A video dice game comprising: a videodisplay device; a cpu having a program operating a dice game; a wagerinput mechanism which registers a wager placed by a player, said wagerincluding an ability to register bets upon successive stages of play ofthe game; a set of differing gameplay element indicia, and a subsetestablished from said set of gameplay element indicia of at least onematch indicia against which representations of dice are to be matched inthe course of play, said dice having a plurality of said gameplayelement indicia thereon as facets of each die; said program establishinga first stage dice toss, and determining whether said first stage tosspresents an advancement condition based upon a match of at least one dieindicium with a match indicium; said program establishing a second stagetoss if a bet has been registered for said second stage toss and apredetermined stage advancement condition is presented by said firststage toss, but if a stage advancement condition is not presented bysaid first stage toss, the game is over and at least a portion of betson said first and second stage tosses are lost; said program including apayout output based upon said wager and predetermined values for saidfirst and second stage tosses according to a preset table.
 73. The videogame of claim 72 wherein beginning with at least said second stage game,said advancement condition is any match between said match indicia andsaid die indicia, with at least one match comprising a winning conditionfor a stage being played, and said program establishes a successivestage toss provided a bet has been registered for a respectivesuccessive stage toss and a winning condition is presented by a nextpreceding stage toss, up to a predetermined n^(th) stage toss.
 74. Thevideo game of claim 73 wherein said program displays said first, secondand successive stages up to said n stage together as discrete arrays onthe visual display, and generates a visual representation of die indiciaresulting from a respective toss on a respective array of said visualdisplay.
 75. The video game of claim 74 wherein said program removesfrom further play any match indicium which is not matched at a stage,and provides a visual representation of any said match indicia remainingin play.
 76. A video dice game comprising: a video display device; a cpuhaving a program operating a dice game; a wager input mechanism whichregisters a wager placed by a player, said wager including an ability toregister bets upon successive stages of play of the game; a set ofdiffering gameplay element indicia; representations of dice having aplurality of said gameplay element indicia thereon as facets of eachdie; said program establishing a first stage dice toss, and determiningwhether said first stage toss presents an advancement condition basedupon a predetermined game format; said program establishing a secondstage toss if a bet has been registered for said second stage toss andan advancement condition is presented by said first stage toss, but ifan advancement condition is not presented by said first stage toss, thegame is over and at least a portion of bets on said first and secondstage tosses are lost; said program including a payout output based uponsaid wager and predetermined values for said first and second stagetosses according to a preset table.
 77. The video game of claim 76wherein said program establishes a successive stage toss provided a bethas been registered for a respective successive stage toss and anadvancement condition is presented by a next preceding stage toss, up toa predetermined n^(th) stage toss.
 78. A method for playing a dice gamecomprising: providing a set of dice having a plurality of differingindicia thereon as facets of each die; establishing a subset from saidindicia of at least one match indicia against which said dice are to bematched in the course of play; placing a bet upon at least one of aplurality of stages of the game, with each stage comprising a toss ofthe dice; making a first stage dice toss, and determining whether saidfirst stage toss presents an advancement condition based upon apredetermined game format; making a second stage toss if a bet has beenregistered for said second stage toss and said predetermined advancementcondition is presented by said first stage toss, but if an advancementcondition is not presented by said first stage toss, the game is overand at least a portion of bets on said first and second stage tosses arelost; providing a payout output based upon said bet(s) and predeterminedvalues for said first and second stage tosses according to a presetschedule.
 79. The dice game method of claim 78 wherein beginning with atleast said second stage game, said advancement condition comprisesdetermining any match between said match indicia and said die indicia,with at least one match comprising an advancement condition for a stagebeing played, and a successive stage toss is made provided a bet hasbeen registered for a respective successive stage toss and anadvancement condition is presented by a next preceding stage toss, up toa predetermined n^(th) stage toss.
 80. A gaming machine comprising: agaming unit having at least first and second stages of play, each saidstage having an advancement condition and a non-advancement condition;an interface mechanism with said gaming unit allowing gameplay input fora player, said gameplay input including wagering input allowing theplayer to register a bet upon one or more stages of play; an operationaldevice operating said gaming unit upon player input including anoperational command, said operational device determining which of saidconditions is presented by a first stage as played, and if anadvancement condition is presented by said first stage as played, thenadvancing said gaming unit to said second stage, but if anon-advancement condition is presented by said first stage as played,the game is over and at least a portion of any second stage betregistered is lost; said operational device operating said gaming unitfor said second stage if an advancement condition is determined for saidfirst stage and a bet has been registered for said second stage, anddetermining which of said conditions is presented by said second stageas played.
 81. The gaming machine of claim 80 wherein said operationaldevice operates said gaming unit for a successive stage up to apredetermined n^(th) stage if an advancement condition is determined forsaid second stage and thereafter for a next preceding stage to saidsuccessive stage, and a bet has been registered for said successivestage, and determining which of said conditions is presented by saidsuccessive stage as played.
 82. The gaming machine of claim 81 furtherincluding a payout device which calculates a payout according to apreset schedule.
 83. The gaming machine of claim 82 wherein said payoutdevice provides a payout for each stage for which an advancementcondition has been determined.
 84. The gaming machine of claim 83wherein said payout device provides a payout multiplier which increasesfor at least some of said second and successive stages.
 85. The gamingmachine of claim 80 wherein said first and second stages of play aregames which are of the same type of game.
 86. The gaming machine ofclaim 85 wherein said type of game is a slot machine device.
 87. Thegaming machine of claim 86 wherein said slot machine device is a videoslot machine having visual representations of plural slot reels.
 88. Thegaming machine of claim 85 wherein said type of game is a card game. 89.The gaming machine of claim 88 wherein said card game is selected fromone of “Draw” and “Stud” poker.
 90. The gaming machine of claim 85wherein said type of game is a dice game.
 91. The gaming machine ofclaim 80 wherein said first and second stages of play are differenttypes of games.
 92. A gaming machine comprising: a gaming unit havingfirst and successive stages of play up to a predetermined n^(th) stage,each said stage having a winning condition and a losing condition; aninterface mechanism with said gaming unit allowing gameplay input for aplayer, said gameplay input including wagering input allowing the playerto register a bet upon one or more stages of play; an operational deviceoperating said gaming unit upon player input including an operationalcommand, said operational device determining which of said winning andlosing conditions is presented by a first stage as played, and if awinning condition is presented by said first stage as played, thenadvancing said gaming unit to a successive stage, but if a losingcondition is presented by said first stage as played, the game is overand at least any successive stage bet registered is lost; saidoperational device operating said gaming unit for said successive stageif a winning condition is determined for a preceding stage and a bet hasbeen registered for said successive stage, and determining which of saidwinning and losing conditions is presented by said successive stage asplayed, up to said n^(th) stage.
 93. The gaming machine of claim 92wherein said gaming unit comprises a slot machine device having visualrepresentations of plural slot reels.
 94. The gaming machine of claim 93wherein a separate slot machine device is visually displayed for eachstage, with a plurality of stages being displayed together.
 95. Thegaming machine of claim 92 wherein said gaming unit comprises a hand ofcards which is visually displayed for each stage, with a plurality ofstages being displayed together.
 96. The gaming machine of claim 92wherein said gaming unit comprises a toss of dice.
 97. The gamingmachine of claim 96 further including a set of differing gameplayelement indicia, and a subset of said set comprising at least one matchindicia against which said dice are to be matched in the course of play,said dice having a plurality of said gameplay element indiciarepresented thereon as facets of each die, and said first and successivestages up to said n^(th) stage are displayed together as discretearrays.
 98. The gaming machine of claim 97 wherein said operationaldevice tosses said dice and beginning with at least said second stage,determines any match between said match indicia and said die indicia,with at least one match comprising a winning condition for a stage beingplayed, and said operational device removes from further play any matchindicium which is not matched at a stage.
 99. The gaming machine ofclaim 98 further including a video display device, said gaming unitgenerating a visual representation of said die indicia resulting from arespective toss on a respective array of said visual display, andgenerating a visual representation of said match indicia remaining inplay.
 100. The gaming machine of claim 92 further including a payoutdevice which provides a payout based upon a table which increases theamount of payout for a given bet as at least some stages are reached.101. The gaming machine of claim 92 further including a feature which issubject to random allocation to a stage in the course of play by saidoperational device, said feature constituting a winning conditionenabling a successive stage to be played regardless of any other winningcondition being presented by a next preceding stage, provided a bet hasbeen placed on said successive stage which is subject to being soenabled for play.
 102. The gaming machine of claim 96 wherein saidoperational device tosses said dice and determines whether said tosspresents a winning condition based upon a predetermined game format.